7. [-/1.5 Points] DETAILS SERCP11 3.2.P.017. MY NOTES A projectile is launched with an initial speed of 40.0 m/s at an angle of 31.0° above the horizontal. The projectile lands on a hillside 3.95 s later. Neglect air friction. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) (a) What is the projectile's velocity at the highest point of its trajectory? magnitude m/s direction º counterclockwise from the +x-axis (b) What is the straight-line distance from where the projectile was launched to where it hits its target? m Need Help? Read It Watch It

To solve this problem, we'll use the principle of conservation of angular momentum and the law of conservation of energy.

Given information:

- Radius of the disk, r = 25.0 cm = 0.25 m

- Rotational inertia of the disk, I = 0.015 kg.m²

- Initial rotation speed, ω₁ = 22.0 rpm

- Mass of the mouse, m = 21.0 g = 0.021 kg

- Distance of the mouse from the center, d = 12.0 cm = 0.12 m

(a) Finding the new rotation speed:

The initial angular momentum of the system is given by:

L₁ = I * ω₁

The final angular momentum of the system is given by:

L₂ = (I + m * d²) * ω₂

According to the conservation of angular momentum, L₁ = L₂. Therefore, we can equate the two expressions for angular momentum:

I * ω₁ = (I + m * d²) * ω₂

Solving for ω₂, the new rotation speed:

ω₂ = (I * ω₁) / (I + m * d²)

Now, let's plug in the given values and calculate ω₂:

ω₂ = (0.015 kg.m² * 22.0 rpm) / (0.015 kg.m² + 0.021 kg * (0.12 m)²)

Note: We need to convert the initial rotation speed from rpm to rad/s since the rotational inertia is given in kg.m².

ω₁ = 22.0 rpm * (2π rad/1 min) * (1 min/60 s) ≈ 2.301 rad/s

ω₂ = (0.015 kg.m² * 2.301 rad/s) / (0.015 kg.m² + 0.021 kg * (0.12 m)²)

Calculating ω₂ will give us the new rotation speed.

(b) Finding the change in kinetic energy:

The initial kinetic energy of the system is given by:

K₁ = (1/2) * I * ω₁²

The final kinetic energy of the system is given by:

K₂ = (1/2) * (I + m * d²) * ω₂²

The change in kinetic energy, ΔK, is given by:

ΔK = K₂ - K₁

Let's plug in the values we already know and calculate ΔK:

ΔK = [(1/2) * (0.015 kg.m² + 0.021 kg * (0.12 m)²) * ω₂²] - [(1/2) * 0.015 kg.m² * 2.301 rad/s²]

Calculating ΔK will give us the change in kinetic energy of the system.

Please note that the provided values are rounded, and for precise calculations, it's always better to use exact values before rounding.

Learn more about angular momentum here: brainly.com/question/29897173

#SPJ11

The alternative that is correct for an elastic collision is that in an elastic collision there is no loss of kinetic energy and no exchange of mass between the bodies involved.

In an elastic collision, the total kinetic energy of the bodies involved in the collision is conserved. This means that there is no loss of kinetic energy during the collision, and all of the kinetic energy of the bodies is still present after the collision. In addition, there is no exchange of mass between the bodies involved in the collision.

This is in contrast to an inelastic collision, where some or all of the kinetic energy is lost as the bodies stick together or deform during the collision. In inelastic collisions, there is often an exchange of mass between the bodies involved as well.

Therefore, the alternative that is correct for an elastic collision is that in an elastic collision there is no loss of kinetic energy and no exchange of mass between the bodies involved.

To know more about elastic collision, refer

https://brainly.com/question/12644900

#SPJ11

The energy required to convert 15.0 grams of ice at -18.4ºC into steam at 126.4ºC is approximately 45,737 Joules.

To convert ice at -18.4ºC into steam at 126.4ºC, we need to consider three steps: the energy required to raise the temperature of the ice to 0ºC, the energy required to melt the ice at 0ºC, and the energy required to raise the temperature of the resulting liquid water from 0ºC to 100ºC.

First, we calculate the energy required to raise the temperature of the ice to 0ºC. The mass of ice is given as 15.0 grams, and the heat capacity of ice is 2.09 J/g·ºC. Using the formula Q = m × c × ΔT, where Q is the energy, m is the mass, c is the heat capacity, and ΔT is the change in temperature, we find that the energy required is 15.0 g × 2.09 J/g·ºC × (0 ºC - (-18.4 ºC)) = 556.8 J.

Next, we calculate the energy required to melt the ice at 0 ºC. The heat of fusion for ice is 334 J/g. So the energy required is 15.0 g × 334 J/g = 5010 J.

Finally, we calculate the energy required to raise the temperature of the resulting liquid water from 0ºC to 10ºC. The heat capacity of water is 4.18 J/g·ºC. Using the same formula as before, we find that the energy required is 15.0 g × 4.18 J/g·ºC × (100ºC - 0ºC) = 6270 J.

Adding up all three steps, we get a total energy requirement of 556.8 J + 5010 J + 6270 J = 11,836.8 J.

To calculate this, we need to consider the heat of vaporization for water, which is 2260 J/g. Since the mass of water vapor is not given, we need to assume that all the water is converted to steam. Therefore, the energy required is 15.0 g × 2260 J/g = 33,900 J.

Adding the energy required for the vaporization step, we get a total energy requirement of 11,836.8 J + 33,900 J = 45,736.8 J.

Hence, the energy required to convert 15.0 grams of ice at -18.4 ºC into steam at 126.4 ºC is approximately 45,737 Joules.

To know more about energy here https://brainly.com/question/2003548

#SPJ4

The work required to move the charges closer together is -1.39 × 10^-18 J (negative because work is done against the electric force).

Given that, Two identical point charges of q = +2.25 x 10-8 C are separated by a distance of 0.85 m.

To find out how much work is required to move them closer together so that they are only 0.40 m apart. So,initial separation between charges = r1 = 0.85 m final separation between charges = r2 = 0.40 mq = +2.25 x 10^-8 C

The potential energy of a system of two point charges can be expressed using the formula as,

U = k * (q1 * q2) / r

where,U is the potential energy

k is Coulomb's constantq1 and q2 are point charges

r is the separation between the two charges

To find the work done, we need to subtract the initial potential energy from the final potential energy, i.e,W = U2 - U1where,W is the work doneU1 is the initial potential energyU2 is the final potential energy

Charge on each point q = +2.25 x 10^-8 C

Coulomb's constant k = 9 * 10^9 N.m^2/C^2

The initial separation between the charges r1 = 0.85 m

The final separation between the charges r2 = 0.40 m

The work done to move the charges closer together is,W = U2 - U1

Initial potential energy U1U1 = k * (q1 * q2) / r1U1 = 9 * 10^9 * (2.25 x 10^-8)^2 / 0.85U1 = 4.2 * 10^-18 J

Final potential energy U2U2 = k * (q1 * q2) / r2U2 = 9 * 10^9 * (2.25 x 10^-8)^2 / 0.4U2 = 2.81 * 10^-18 J

Work done W = U2 - U1W = 2.81 * 10^-18 - 4.2 * 10^-18W = -1.39 * 10^-18 J

To know more about work:

https://brainly.com/question/18094932

#SPJ11

The required wind speed in the wind tunnel is approximately 20 mph.

To determine the required wind speed in the wind tunnel, we need to consider the scale ratio between the model and the actual house. The given length scale for the home is 30 feet, while the model is built at a length scale of 5 feet. Therefore, the scale ratio is 30/5 = 6.

Given that the hurricane wind speeds are 100 mph, we can calculate the wind speed in the wind tunnel by dividing the actual wind speed by the scale ratio. Thus, the required wind speed in the wind tunnel would be 100 mph / 6 = 16.7 mph.

However, we also need to take into account the operating conditions of the wind tunnel. The wind tunnel is operating at 7 atm absolute pressure, which is equivalent to approximately 101.3 psi. Under these high-pressure conditions, the viscosity of air becomes different compared to one atmosphere conditions.

Fortunately, the question states that the viscosity of air in the wind tunnel at 7 atm is nearly the same as at one atmosphere. This allows us to assume that the air viscosity remains constant, and we can use the same wind speed calculated previously.

To summarize, the required wind speed in the wind tunnel to test various construction methods for protecting single-family homes from hurricane force winds would be approximately 20 mph, considering the given scale ratio and the assumption of similar air viscosity.

Learn more about wind speed

brainly.com/question/12005342

#SPJ11

The car is not speeding. The speed of 39 m/s is equivalent to approximately 87.2 mi/hr.

Since the speed limit is 65.0 mi/hr, the driver is not exceeding the speed limit. Therefore, the driver is within the legal speed limit and does not need to slow down. To convert the speed from m/s to mi/hr, we can use the conversion factor 1 mi = 1609 m and 1 hr = 3600 s. So, 39 m/s is equal to (39 m/s) * (1 mi / 1609 m) * (3600 s / 1 hr) ≈ 87.2 mi/hr. Hence, the driver is not speeding and is within the speed limit.

To learn more about speed:

https://brainly.com/question/28224010

#SPJ11

The correct answers are (a) 7.53 m/s, (b) 8.19 m/s, and (c) 5.00 m/s. The average speed is calculated as follows: v_avg = sum_i v_i / N

where v_avg is the average speed

v_i is the speed of particle i

N is the number of particles

Plugging in the given values, we get

v_avg = (4.00 m/s + 2 * 5.00 m/s + 3 * 7.00 m/s + 4 * 5.00 m/s + 3 * 10.0 m/s + 2 * 14.0 m/s) / 15

= 7.53 m/s

The rms speed is calculated as follows:

v_rms = sqrt(sum_i (v_i)^2 / N)

Plugging in the given values, we get

v_rms = sqrt((4.00 m/s)^2 + 2 * (5.00 m/s)^2 + 3 * (7.00 m/s)^2 + 4 * (5.00 m/s)^2 + 3 * (10.0 m/s)^2 + 2 * (14.0 m/s)^2) / 15

= 8.19 m/s

The most probable speed is the speed at which the maximum number of particles are found. In this case, the most probable speed is 5.00 m/s.

Learn more about rms speed here:

brainly.com/question/33262591

#SPJ11

When a proton is placed at rest some distance from a charged object and experiences a potential of 45 V, the proton will move to a place where there is lower potential. The correct answer is option c.

The potential experienced by a charged particle determines its movement. A positively charged proton will naturally move towards a region with lower potential energy. In this case, as the proton experiences a potential of 45 V, it will move towards a region where the potential is lower.

This movement occurs because charged particles tend to move from higher potential to lower potential in order to minimize their potential energy.

Therefore, the correct statement is that the proton will move to a place where there is lower potential. Option c is correct.

To know more about proton, click here-

brainly.com/question/12535409

#SPJ11

Converting the energy consumption of the E-scooter into gigajoules, we find that one can travel around the Earth approximately 11,360 times using 1.228x10^2 GJ of energy with the E-scooter.

First, we convert the energy consumption of the E-scooter from kilowatt-hours (kWh) to gigajoules (GJ).

1 kilowatt-hour (kWh) = 3.6 megajoules (MJ)

1 gigajoule (GJ) = 1,000,000 megajoules (MJ)

So, the energy consumption of the E-scooter per 100 km is:

3 kWh * 3.6 MJ/kWh = 10.8 MJ (megajoules)

Now, we calculate the number of trips around the Earth.

The Earth's circumference is approximately 40,075 kilometers.

Energy consumed per trip = 10.8 MJ

Total energy available = 1.228x10^2 GJ = 1.228x10^5 MJ

Number of trips around the Earth = Total energy available / Energy consumed per trip

= (1.228x10^5 MJ) / (10.8 MJ)

= 1.136x10^4

Therefore, approximately 11,360 times one can travel around the Earth using 1.228x10^2 GJ of energy with the E-scooter.

To know more about energy consumption, refer to the link :

https://brainly.com/question/30125850#

#SPJ11

To correct the nearsightedness of a person with a far point at 157 cm, lenses with a power of approximately -0.636 diopters (concave) should be prescribed. Consultation with an eye care professional is important for an accurate prescription and fitting.

To determine the power of lenses required to correct the nearsightedness of a person, we can use the formula:

Lens Power (in diopters) = 1 / Far Point (in meters)

Given that the far point of the nearsighted person is 157 cm (which is 1.57 meters), we can substitute this value into the formula:

Lens Power = 1 / 1.57 = 0.636 diopters

Therefore, a nearsighted person with a far point at 157 cm would require lenses with a power of approximately -0.636 diopters. The negative sign indicates that the lenses need to be concave (diverging) in nature to help correct the person's nearsightedness.

These lenses will help diverge the incoming light rays, allowing them to focus properly on the retina, thus improving distance vision for the individual. It is important for the individual to consult an optometrist or ophthalmologist for an accurate prescription and proper fitting of the lenses based on their specific needs and visual acuity.

To learn more about lenses

https://brainly.com/question/28039799

#SPJ11

The change in refractive index of the glucose solution is 2.34.

Michelson interferometer is an instrument used to measure the refractive index of a substance. It uses a laser beam that is divided into two equal parts, and each part travels a different path before recombining to produce an interference pattern on a screen.

A cuvette of thickness 10 mm is placed in one arm containing a glucose solution. As the glucose concentration increases, 88 fringes are observed to emerge at the screen. We need to determine the change in refractive index of the glucose solution.

The fringe order is given by:

n = (2t/λ) * δwhere,

t = thickness of the cuvette

λ = wavelength of the laser

δ = refractive index of the glucose solution

Since we know the values of t, λ and n, we can solve for

δδ = (nλ) / (2t)

= (88 × 530 nm) / (2 × 10 mm)

= 2.34

Therefore, the  change in refractive index of the glucose solution is 2.34.

Learn more about refractive index, here

https://brainly.com/question/83184

#SPJ11

The formula for the conductivity of a band with cubic symmetry given in (13.71) is e2 o 121.

The h T(E)US, (13.71)where S is the area of Fermi surface in the band, and v is the electronic speed averaged over the Fermi surface: (13.72) ſas pras.The question requires us to verify that (13.71) reduces to the Drude result in the free electron limit. The Drude result states that the conductivity of a metal in the free electron limit is given by the following formula:σ = ne2τ/mwhere n is the number of electrons per unit volume, τ is the average time between collisions of an electron, m is the mass of the electron, and e is the charge of an electron. In the free electron limit, the Fermi energy is much larger than kBT, where kB is the Boltzmann constant.

This means that the Fermi-Dirac distribution function can be approximated by a step function that is 1 for energies below the Fermi energy and 0 for energies above the Fermi energy. In this limit, the integral over k in (13.25) reduces to a sum over states at the Fermi surface. Therefore, we can write (13.25) as follows:σ = Σση) = ne2τ/mwhere n is the number of electrons per unit volume, τ is the average time between collisions of an electron, m is the mass of the electron, and e is the charge of an electron. Comparing this with (13.71), we see that it reduces to the Drude result in the free electron limit. Therefore, we have verified that (13.71) reduces to the Drude result in the free electron limit.

To know more about conductivity:

https://brainly.com/question/31201773

#SPJ11

The internal resistance of the battery is 4.0 ohms. We can use Ohm's Law and the formula for the potential difference across a resistor.

To calculate the internal resistance of the battery, we can use Ohm's Law and the formula for the potential difference across a resistor.

Ohm's Law states that the potential difference (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R):

V = I * R

In this case, the potential difference across the battery terminals is given as 10.0 volts, and the current flowing through the load is 0.500 ampere.

However, the potential difference across the battery terminals is not equal to the emf (E) of the battery due to the presence of internal resistance (r). The relation between the terminal voltage (Vt), emf (E), and internal resistance (r) can be given as:

Vt = E - I * r

where Vt is the potential difference across the battery terminals, E is the emf of the battery, I is the current flowing through the load, and r is the internal resistance of the battery.

Given that Vt = 10.0 volts and E = 12.0 volts, we can substitute these values into the equation:

10.0 volts = 12.0 volts - 0.500 ampere * r

Simplifying the equation, we have:

0.500 ampere * r = 12.0 volts - 10.0 volts

0.500 ampere * r = 2.0 volts

Dividing both sides of the equation by 0.500 ampere, we get:

r = 2.0 volts / 0.500 ampere

r = 4.0 ohms

Therefore, the internal resistance of the battery is 4.0 ohms.

To learn more about Ohm's Law click here

https://brainly.com/question/1247379

#SPJ11

The maximum frequency of the sound that reaches the listener is approximately 712.286 Hz. The beat frequency heard in the problem mentioned in Part A is approximately 224.571 Hz.

Radius of the carousel (r) = 5.00 m

Frequency of the sirens (f) = 600 Hz

Angular velocity of the carousel (ω) = 0.800 rad/s

Speed of sound (v) = 350 m/s

(a) The maximum frequency occurs when the siren is moving directly towards the listener. In this case, the Doppler effect formula for frequency can be used:

f' = (v +[tex]v_{observer[/tex]) / (v + [tex]v_{source[/tex]) * f

Since the carousel is rotating, the velocity of the observer is equal to the tangential velocity of the carousel:

[tex]v_{observer[/tex] = r * ω

The velocity of the source is the velocity of sound:

[tex]v_{source[/tex]= v

Substituting the given values:

f' = (v + r * ω) / (v + v) * f

f' = (350 m/s + 5.00 m * 0.800 rad/s) / (350 m/s + 350 m/s) * 600 Hz

f' ≈ 712.286 Hz

Therefore, the maximum frequency of the sound that reaches the listener is approximately 712.286 Hz.

(b) Minimum Frequency of the Sound:

The minimum frequency occurs when the siren is moving directly away from the listener. Using the same Doppler effect formula:

f' = (v + [tex]v_{observer)[/tex] / (v - [tex]v_{source)[/tex] * f

Substituting the values:

f' = (v + r * ω) / (v - v) * f

f' = (350 m/s + 5.00 m * 0.800 rad/s) / (350 m/s - 350 m/s) * 600 Hz

f' ≈ 487.714 Hz

Therefore, the minimum frequency of the sound that reaches the listener is approximately 487.714 Hz.

(c) The beat frequency is the difference between the maximum and minimum frequencies:

Beat frequency = |maximum frequency - minimum frequency|

Beat frequency = |712.286 Hz - 487.714 Hz|

Beat frequency ≈ 224.571 Hz

Therefore, the beat frequency heard in the problem mentioned in Part A is approximately 224.571 Hz.

(d) In this case, when the maximum beat frequency is heard, one siren is behind the other. The sirens and the listener form an isosceles triangle, with both sirens being equidistant to the listener.

Learn more about sound here:

https://brainly.com/question/30045405

#SPJ11

The total impulse delivered to the box by the 10 collisions is 0.006 kg·m/s, the total change in momentum of the 100 g box is 0.012 kg·m/s, and the total change in velocity of the 100 g box after these 10 collisions is 0.12 m/s.

The total impulse delivered to the box by the 10 collisions can be calculated using the equation:

Impulse = Change in Momentum

First, let's calculate the momentum of each 2.0 g ball. The momentum of an object is given by the equation:

Momentum = mass x velocity

Since the mass of each ball is 2.0 g and the velocity is 30 cm/s, we convert the mass to kg and the velocity to m/s:

mass = 2.0 g = 0.002 kg
velocity = 30 cm/s = 0.3 m/s

Now, we can calculate the momentum of each ball:

Momentum = 0.002 kg x 0.3 m/s = 0.0006 kg·m/s

Since 10 balls are shot in succession, the total impulse delivered to the box is the sum of the impulses from each ball. Therefore, we multiply the momentum of each ball by the number of balls (10) to find the total impulse:

Total Impulse = 0.0006 kg·m/s x 10 = 0.006 kg·m/s

Next, let's calculate the total change in momentum of the 100 g box. The initial momentum of the box is zero since it is at rest. After each collision, the box gains momentum in the opposite direction to the ball's momentum. Since the box rebounds off the ball with the same momentum, the change in momentum for each collision is twice the momentum of the ball. Therefore, the total change in momentum of the box is:

Total Change in Momentum = 2 x Total Impulse = 2 x 0.006 kg·m/s = 0.012 kg·m/s

Finally, let's calculate the total change in velocity of the 100 g box after these 10 collisions. The change in velocity can be found using the equation:

Change in Velocity = Change in Momentum / Mass

The mass of the box is 100 g = 0.1 kg. Therefore, the total change in velocity is:

Total Change in Velocity = Total Change in Momentum / Mass = 0.012 kg·m/s / 0.1 kg = 0.12 m/s

Therefore, the total impulse delivered to the box by the 10 collisions is 0.006 kg·m/s, the total change in momentum of the 100 g box is 0.012 kg·m/s, and the total change in velocity of the 100 g box after these 10 collisions is 0.12 m/s.

To more about velocity visit:

https://brainly.com/question/34025828

#SPJ11

The electrical resistance of a 20.0 m length of tungsten wire of radius 0.200 mm, when the resistivity of tungsten is 5.6×10^-8 Ω⋅m can be determined using the following steps:

1: Find the cross-sectional area of the wire The cross-sectional area of the wire can be calculated using the formula for the area of a circle, which is given by: A

= πr^2where r is the radius of the wire. Substituting the given values: A

= π(0.0002 m)^2A

= 1.2566 × 10^-8 m^2given by: R

= ρL/A Substituting

= (5.6 × 10^-8 Ω⋅m) × (20.0 m) / (1.2566 × 10^-8 m^2)R

= 1.77 Ω

To know more about resistivity visit:

https://brainly.com/question/29427458

#SPJ11

The student should locate the camera at the focal point of the concave mirror to create an astronomical telescope for capturing pictures of distant galaxies.

In order to create an astronomical telescope using a concave mirror, the camera should be placed at the focal point of the mirror.

This is because a concave mirror converges light rays, and placing the camera at the focal point allows it to capture the converging rays from distant galaxies. By positioning the camera at the focal point, the telescope will produce clear and magnified images of the galaxies.

Placing the camera infinitely far from the mirror would not allow for focusing, while placing it near the center of curvature or on the mirror's surface would not provide the desired image formation.

To learn more about concave mirror click here: brainly.com/question/31379461

#SPJ11

The magnitude of the force on the wire is 1.9 × 10⁻⁴ N. The direction of the current is 50° south of the west. 1.9×10 N⁻⁴, out of the Earth's surface is the correct option.

Length of the horizontal wire, L = 3.0 m

Current flowing through the wire, I = 6.0 A

Earth's magnetic field, B = 0.14 × 10⁻⁴ T

Angle made by the current direction with due west = 50° south of westForce on a current-carrying wire due to the Earth's magnetic field is given by the formula:

F = BILsinθ, where

L is the length of the wire, I is the current flowing through it, B is the magnetic field strength at that location and θ is the angle between the current direction and the magnetic field direction

Magnitude of the force on the wire is

F = BILsinθF = (0.14 × 10⁻⁴ T) × (6.0 A) × (3.0 m) × sin 50°F = 1.9 × 10⁻⁴ N

Earth's magnetic field is due north, the direction of the force on the wire is out of the Earth's surface. Therefore, the correct option is 1.9×10 N⁻⁴, out of the Earth's surface.

You can learn more about magnitude at: brainly.com/question/31022175

#SPJ11

The mass of the neutral atom, considering a nucleus with 68 protons and 92 neutrons, a binding energy per nucleon of 3.82 MeV, and the provided atomic mass units, appears to be -449.780444 u.

To calculate the mass of the neutral atom, we need to consider the masses of protons and neutrons, as well as the number of protons and neutrons in the nucleus.

Number of protons (Z) = 68

Number of neutrons (N) = 92

Binding energy per nucleon (BE/A) = 3.82 MeV

Proton mass = 1.007277 u

Neutron mass = 1.008665 u

Atomic mass unit (u) = 931.494 MeV/c²

let's calculate the total number of nucleons (A) in the nucleus:

A = Z + N

A = 68 + 92

A = 160

we can calculate the total binding energy (BE) of the nucleus:

BE = BE/A * A

BE = 3.82 MeV * 160

BE = 611.2 MeV

let's calculate the mass of the neutral atom in atomic mass units (u):

Mass = (Z * proton mass) + (N * neutron mass) - BE/u

Mass = (68 * 1.007277 u) + (92 * 1.008665 u) - (611.2 MeV / 931.494 MeV/c²)

Converting MeV to u using the conversion factor (1 MeV/c² = 1/u):

Mass ≈ (68 * 1.007277 u) + (92 * 1.008665 u) - (611.2 u)

Mass ≈ 68.476876 u + 92.94268 u - 611.2 u

Mass ≈ -449.780444 u

Learn more about binding energy: brainly.com/question/10095561

#SPJ11

Horizontal displacement = 4008 meters

The launch angle should be approximately 20.5°

To find how far away the target is, the horizontal displacement of the shell needs to be found.

This can be done using the formula:

horizontal displacement = initial horizontal velocity x time

The time taken for the shell to reach the ground can be found using the formula:

vertical displacement = initial vertical velocity x time + 0.5 x acceleration x time^2

Since the shell is fired horizontally, its initial vertical velocity is 0. The acceleration due to gravity is 9.8 m/s^2. The vertical displacement is -150 m (since it is below the cliff).

Using these values, we get:-150 = 0 x t + 0.5 x 9.8 x t^2

Solving for t, we get:t = 5.01 seconds

The horizontal displacement is therefore:

horizontal displacement = 800 x 5.01

horizontal displacement = 4008 meters

3. To find the launch angle, we can use the formula:

Δy = (v^2 x sin^2 θ)/2g Where Δy is the vertical displacement (26 ft), v is the initial velocity (30 ft/s), g is the acceleration due to gravity (32 ft/s^2), and θ is the launch angle.

Using these values, we get:26 = (30^2 x sin^2 θ)/2 x 32

Solving for sin^2 θ:sin^2 θ = (2 x 26 x 32)/(30^2)sin^2 θ = 0.12

Taking the square root:sin θ = 0.35θ = sin^-1 (0.35)θ = 20.5°

Therefore, the launch angle should be approximately 20.5°.

Note: The given measurements are in feet, but the calculations are done in fps (feet per second).

Learn more about horizontal displacement here https://brainly.com/question/6107697

#SPJ11

The force corresponding to the potential energy function U(x) = -a/x + b/[tex]x^{2}[/tex] + c[tex]x^{2}[/tex] can be obtained by taking the derivative of the potential energy function with respect to x.  The force corresponding to the potential energy function is  F(x) = a/[tex]x^{2}[/tex] - 2b/[tex]x^{3}[/tex] + 2cx.

To find the force corresponding to the potential energy function, we differentiate the potential energy function with respect to position (x). In this case, we have U(x) = -a/x + b/[tex]x^{2}[/tex] + c[tex]x^{2}[/tex].

Taking the derivative of U(x) with respect to x, we obtain:

dU/dx = -(-a/[tex]x^{2}[/tex]) + b(-2)/[tex]x^{3}[/tex] + 2cx

Simplifying the expression, we get:

dU/dx = a/[tex]x^{2}[/tex] - 2b/[tex]x^{3}[/tex] + 2cx

This expression represents the force corresponding to the potential energy function U(x). The force is a function of position (x) and is determined by the specific values of the constants a, b, and c in the potential energy function.

To learn more about potential energy click here:

brainly.com/question/1455245

#SPJ11

An ice cube of volume 50 cm³ is initially at the temperature of 250K. Let's find out how much heat is required to convert this ice cube into room temperature (300 K)

Solution:

It is given that the initial temperature of the ice cube is 250K and it has to be converted to room temperature (300K).

Now, we know that to convert ice at 0°C to water at 0°C, heat is required and the quantity of heat required is given byQ = mL

where, Q = Quantity of heat required, m = Mass of ice/water and L = Latent heat of fusion of ice at 0°C.

Now, to convert ice at 0°C to water at 0°C, heat is required.

The quantity of heat required is given by:

Q1 = mL1

Where, m = mass of ice

= Volume of ice × Density of ice

= (50/1000) × 917 = 45.85g(1 cm³ of ice weighs 0.917 g)

L1 = Latent heat of fusion of ice = 3.34 × 10⁵ J/kg (at 0°C)

Therefore,

Q1 = mL1 = (45.85/1000) × 3.34 × 10⁵

= 153.32 J

Now, the water formed at 0°C has to be heated to 300K (room temperature).

Heat required is given byQ2 = mCΔT

Where, m = mass of water

= 45.85 g (from above)

C = specific heat capacity of water = 4.2 J/gK (at room temperature)

ΔT = Change in temperature = (300 - 0) K

= 300 K

T = Temperature of water at room temperature = 300K

Therefore, Q2 = mCΔT= 45.85 × 4.2 × 300= 57834 J

Therefore, total heat required = Q1 + Q2= 153.32 J + 57834 J= 57987.32 J

Hence, the heat required to convert the ice cube of volume 50 cm³ at a temperature of 250K to water at a temperature of 300K is 57987.32 J.

To know more about temperature visit :

https://brainly.com/question/7510619

#SPJ11

The mass of ice remaining at thermal equilibrium is approximately 0.125 kg, assuming no heat loss or gain from the environment.

To calculate the mass of ice that remains at thermal equilibrium, we need to consider the heat exchange that occurs between the ice and water.

The heat lost by the water is equal to the heat gained by the ice during the process of thermal equilibrium.

The heat lost by the water is given by the formula:

Heat lost by water = mass of water * specific heat of water * change in temperature

The specific heat of water is approximately 4.186 kJ/(kg·°C).

The heat gained by the ice is given by the formula:

Heat gained by ice = mass of ice * latent heat of fusion

The latent heat of fusion for ice is 334 kJ/kg.

Since the system is in thermal equilibrium, the heat lost by the water is equal to the heat gained by the ice:

mass of water * specific heat of water * change in temperature = mass of ice * latent heat of fusion

Rearranging the equation, we can solve for the mass of ice:

mass of ice = (mass of water * specific heat of water * change in temperature) / latent heat of fusion

Given:

Plugging in the values:

mass of ice = (1 kg * 4.186 kJ/(kg·°C) * 24°C) / 334 kJ/kg

mass of ice ≈ 0.125 kg (to 3 decimal places)

Therefore, the mass of ice that remains at thermal equilibrium is approximately 0.125 kg.

The complete question should be:

Calculate the mass of ice that remains at thermal equilibrium when 1 kg of ice at -43°C is added to 1 kg of water at 24°C.

Please report the mass of ice in kg to 3 decimal places.

Hint: the latent heat of fusion is 334 kJ/kg, and you should assume no heat is lost or gained from the environment.

To learn more about thermal equilibrium, Visit:

https://brainly.com/question/14556352

#SPJ11

The oxygen molecule is estimated to travel approximately 0.94248 nm during a 1.00-second time interval in air at atmospheric pressure and 18.3°C.

To estimate the total distance traveled by an oxygen molecule during a 1.00-second time interval,

We need to consider its average speed and the time interval.

The average speed of a molecule can be calculated using the formula:

Average speed = Distance traveled / Time interval

The distance traveled by the oxygen molecule can be approximated as the circumference of a circle with a diameter of 0.300 nm.

The formula for the circumference of a circle is:

Circumference = π * diameter

Given:

Diameter = 0.300 nm

Substituting the value into the formula:

Circumference = π * 0.300 nm

To calculate the average speed, we also need to convert the time interval into seconds.

Given that the time interval is 1.00 second, we can proceed with the calculation.

Now, we can calculate the average speed using the formula:

Average speed = Circumference / Time interval

Average speed = (π * 0.300 nm) / 1.00 s

To estimate the total distance traveled, we multiply the average speed by the time interval:

Total distance traveled = Average speed * Time interval

Total distance traveled = (π * 0.300 nm) * 1.00 s

Now, we can approximate the value using the known constant π and convert the result to a more appropriate unit:

Total distance traveled ≈ 0.94248 nm

Therefore, the oxygen molecule is estimated to travel approximately 0.94248 nm during a 1.00-second time interval in air at atmospheric pressure and 18.3°C.

Learn more about Oxygen from the given link :

https://brainly.com/question/4030823

#SPJ11

Explanation:

We can use Faraday's law of electromagnetic induction to solve this problem. According to this law, the induced emf (ε) in a coil is equal to the negative of the rate of change of magnetic flux through the coil:

ε = - dΦ/dt

where Φ is the magnetic flux through the coil.

Rearranging this equation, we can solve for the magnetic flux:

dΦ = -ε dt

Integrating both sides of the equation, we get:

Φ = - ∫ ε dt

Since the emf and the rate of current change are constant, we can simplify the integral:

Φ = - ε ∫ dt

Φ = - ε t

Substituting the given values, we get:

ε = 15.0 mV = 0.0150 V

N = 513

di/dt = 10.0 A/s

i = 3.80 A

We want to find the magnetic flux through each turn of the coil at an instant when the current is 3.80 A. To do this, we first need to find the time interval during which the current changes from 0 A to 3.80 A:

Δi = i - 0 A = 3.80 A

Δt = Δi / (di/dt) = 3.80 A / 10.0 A/s = 0.380 s

Now we can use the equation for magnetic flux to find the flux through each turn of the coil:

Φ = - ε t = -(0.0150 V)(0.380 s) = -0.00570 V·s

The magnetic flux through each turn of the coil is equal to the total flux divided by the number of turns:

Φ/ N = (-0.00570 V·s) / 513

Taking the magnitude of the result, we get:

|Φ/ N| = 1.11 × 10^-5 V·s/turn

Therefore, the magnetic flux through each turn of the coil at the given instant is 1.11 × 10^-5 V·s/turn.

The gauge pressure on a scuba diver swimming at a depth of 17.0 m below the surface of a saltwater sea can be calculated using the given information.

To find the gauge pressure on the diver, we need to consider the pressure due to the depth of the water and subtract the atmospheric pressure.

Pressure due to depth: The pressure at a given depth in a fluid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

In this case, the depth is 17.0 m, and the density of saltwater is 1.03 g/cm³.

Conversion of units: Before substituting the values into the equation, we need to convert the density from g/cm³ to kg/m³ and the atmospheric pressure from in HG to atmospheres.

Density conversion: 1.03 g/cm³ = 1030 kg/m³Atmospheric pressure conversion: 1 in HG = 0.0334211 atmospheres (approx.)

Calculation: Now we can substitute the values into the equation to find the pressure due to depth.P = (1030 kg/m³) * (9.8 m/s²) * (17.0 m) = 177470.0 N/m²

Subtracting atmospheric pressure: To find the gauge pressure, we subtract the atmospheric pressure from the pressure due to depth.

Gauge pressure = Pressure due to depth - Atmospheric pressure

Gauge pressure = 177470.0 N/m² - (29.92 in HG * 0.0334211 atmospheres/in HG)

To learn more about gauge pressure click here.

brainly.com/question/30698101

#SPJ11

The spring constant of Jayden's bungee cord is approximately 104.125 N/m.

To find the spring constant of the bungee cord, we can utilize Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In this case, the displacement is the difference in length between the unstretched and stretched bungee cord.

The change in length of the bungee cord during Jayden's jump can be calculated as follows:

Change in length = Stretched length - Unstretched length

= 33 m - 25 m

= 8 m

Now, Hooke's law can be expressed as:

F = k * x

where F is the force exerted by the spring, k is the spring constant, and x is the displacement.

Since Jayden is at rest when suspended, the net force acting on him is zero. Therefore, the force exerted by the bungee cord must balance Jayden's weight. The weight can be calculated as:

Weight = mass * acceleration due to gravity

= 85 kg * 9.8 m/s^2

= 833 N

Using Hooke's law and setting the force exerted by the bungee cord equal to Jayden's weight:

k * x = weight

Substituting the values we have:

k * 8 m = 833 N

Solving for k:

k = 833 N / 8 m

= 104.125 N/m

Therefore, the spring constant of Jayden's bungee cord is approximately 104.125 N/m.

To learn more about spring constant

https://brainly.com/question/23885190

#SPJ11

According to the junction rule, the current entering junction 1 is equal to the sum of the currents leaving junction 1: I1 = I3 + I4.

The junction rule, or Kirchhoff's current law, states that the total current flowing into a junction is equal to the total current flowing out of that junction. In this case, at junction 1, the current I1 is equal to the sum of the currents I3 and I4. This rule is based on the principle of charge conservation, where the total amount of charge entering a junction must be equal to the total amount of charge leaving the junction. Applying the loop rule, or Kirchhoff's voltage law, we can analyze the potential differences around the loops in the circuit. In the left circuit, traversing the loop in a clockwise direction, we encounter the potential differences V0, -I3R3, -I3R2, and -I1R1. According to the loop rule, the algebraic sum of these potential differences must be zero to satisfy the conservation of energy. This equation relates the currents I1 and I3 and the voltages across the resistors in the left circuit. Similarly, in the right circuit, traversing the loop in a clockwise direction, we encounter the potential differences -I4R4, I3R3, and I3R3. Again, the loop rule states that the sum of these potential differences must be zero, providing a relationship between the currents I3 and I4.

To learn more about Kirchhoff's current law, Click here:

https://brainly.com/question/30394835

#SPJ11

The question is related to the phenomenon of eyeshine exhibited by many nocturnal animals. The animals' eyes react in a particular way due to a thin layer of reflective tissue called the tapetum lucidum that is present directly behind the retina.

This tissue reflects the light back through the retina, which increases the available light that can activate photoreceptors and, thus, improve the animal's vision in low-light conditions.We need to calculate the distance at which an image would be formed of an object situated 30.0 cm away from the tapetum lucidum if we assume the tapetum lucidum acts like a concave spherical mirror with a radius of curvature of 0.750 cm. Neglect the effects of aberrations. Therefore, by applying the mirror formula we get the main answer as follows:

1/f = 1/v + 1/u

Here, f is the focal length of the mirror, v is the image distance, and u is the object distance. It is given that the radius of curvature, r = 0.750 cm

Hence,

f = r/2

f = 0.375 cm

u = -30.0 cm (The negative sign indicates that the object is in front of the mirror).

Using the mirror formula, we have:

1/f = 1/v + 1/u

We get: v = 0.55 cm

Therefore, an image of the object would be formed 0.55 cm in front of the tapetum lucidum. Hence, in conclusion we can say that the Image will form at 0.55 cm in front of the tapetum lucidum.

to know more about nocturnal animals visit:

brainly.com/question/31402222

#SPJ11

The speed of the ball just before it hits the ground is 28 m/s.

We can solve the given problem by using the following kinematic equation: v² = u² + 2as.

Here, v is the final velocity of the ball, u is the initial velocity of the ball, a is the acceleration due to gravity, and s is the vertical displacement of the ball from its launch point.

Let us first calculate the time taken by the ball to hit the ground:

Using the formula, s = ut + 1/2 at²

Where u = 0 (as the ball is thrown horizontally), s = 0.7 km = 700 m, and a = g = 9.8 m/s²

So, 700 = 0 + 1/2 × 9.8 × t²

Or, t² = 700/4.9 = 142.85

Or, t = sqrt(142.85) = 11.94 s

Now, we can use the horizontal displacement of the ball to find its initial velocity:

u = s/t = 63/11.94 = 5.27 m/s

Finally, we can use the kinematic equation to find the final velocity of the ball:

v² = u² + 2as = 5.27² + 2 × 9.8 × 700 = 27.8²

So, v = sqrt(27.8²) = 27.8 m/s

Therefore, the speed of the ball (m/s) just before it hits the ground is approximately 28 m/s.

To learn more about speed, refer below:

https://brainly.com/question/17661499

#SPJ11