you toss a racquetball directly upward and then catch it at the same height you released it 1.56 s later. assume air resistance is negligible. (a) what is the acceleration of the ball while it is moving upward? magnitude m/s2 direction ---select--- (b) what is the acceleration of the ball while it is moving downward? magnitude m/s2 direction ---select--- (c) what is the acceleration of the ball while it is at its maximum height? magnitude m/s2 direction ---select--- (d) what is the velocity of the ball when it reaches its maximum height? magnitude m/s direction ---select--- (e) what is the initial velocity of the ball? magnitude m/s direction ---select--- (f) what is the maximum height that the ball reaches?

The pitching speed of the player to cover a horizontal distance of 20 m when the ball is thrown horizontally from a height of 5 m is 19.82 m/s.

To find the pitching speed, we need to use the kinematic equation, which relates the distance traveled by an object to its initial velocity and the time it takes to travel that distance.

Since the ball is thrown horizontally, we can assume that the initial velocity of the ball is horizontal and the acceleration of the ball is vertical due to the force of gravity.

Using the equation of motion for the horizontal motion:

distance = speed × time

Since the ball is thrown horizontally, there is no initial vertical velocity, so the initial velocity is zero.

Therefore, distance = speed × time

time = distance/speed

Using the equation of motion for the vertical motion:

[tex]distance = initial \ velocity \times time + (1/2) \times acceleration \times time^2[/tex]

Since the ball is thrown horizontally, the initial vertical velocity is zero, and the acceleration due to gravity is 9.81 m/s² (since it is acting downward).

Therefore, [tex]distance = (1/2) \times (9.81) \times time^2[/tex]

[tex]time^2 = 2 \times distance/9.81[/tex]

[tex]time = \sqrt{2 \times distance / acceleration}[/tex]

Substituting the values

[tex]time = \sqrt{2\times(5/9.81)} = 1.009 s[/tex]

Now, substituting the value of time in the horizontal motion equation:

[tex]speed = distance/time[/tex]

[tex]speed = 20/1.009 = 19.82\  m/s[/tex]

Speed = 19.82 m/s

Therefore, the player's pitching speed is 19.82 m/s.

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580 nm light shines on a double slit with d=0. 000125 m. the angle of the third dark interference minimum(m=3) is 0.76 degrees.

The angle θ of the third dark interference minimum can be calculated using the equation:

sin θ = (m λ) / d

where m is the order of the interference minimum, λ is the wavelength of the light, and d is the distance between the slits.

In this case, m = 3, λ = 580 nm = 5.80 × 10^−7 m, and d = 0.000125 m. Plugging in these values, we get:

sin θ = (3 × 5.80 × 10^−7 m) / 0.000125 m

solving this, we get:

sin θ = 0.0132

Taking the inverse sine of both sides, we get:

θ = sin−1 (0.0132)

Using a calculator, we find:

θ ≈ 0.76 degrees

Therefore, the angle of the third dark interference minimum is approximately 0.76 degrees.

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The apprοximate speed οf the rοller cοaster at the bοttοm οf the track is 31.6 m/s.

It is defined as the distance travelled by an οbject per unit time, and is usually expressed in meters per secοnd (m/s) οr οther units οf distance per unit time (such as miles per hοur οr kilοmeters per hοur).

Nο, the speed οf the rοller cοaster at the bοttοm οf the track is nοt 45 m/s.

Tο determine the speed οf the rοller cοaster at the bοttοm οf the track, we can use the principle οf cοnservatiοn οf energy, which states that the tοtal amοunt οf energy in a clοsed system remains cοnstant.

At the tοp οf the track, the rοller cοaster has οnly pοtential energy, which can be calculated as: PE = mgh

where m is the mass οf the rοller cοaster, g is the acceleratiοn due tο gravity (apprοximately 9.81 m/s²), and h is the height οf the track (51 meters). Assuming the mass οf the rοller cοaster is 1 kilοgram, the pοtential energy at the tοp οf the track is :

[tex]PE = (1 kg)(9.81 m/s^2)(51 m) = 502.31 J[/tex]

At the bottom of the track, all of the potential energy has been converted to kinetic energy, which can be calculated as:

[tex]KE = 1/2 mv^2[/tex]

where v is the speed of the roller coaster. Equating the initial potential energy to the final kinetic energy, we have:

PE = KE

[tex]mgh = 1/2 mv^2Solving for v, we get:v = sqrt(2gh)v = sqrt(2 x 9.81 m/s^2 x 51 m) = sqrt(999.162) = 31.6 m/s (approximately)[/tex]

Therefore, the approximate speed of the roller coaster at the bottom of the track is 31.6 m/s.

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The type of reflection occurring when light hits a surface can be determined by observing how the light is scattered.

Specular reflection occurs when light is reflected at a single angle, resulting in a clear and focused reflection. On the other hand, diffuse reflection occurs when light is scattered in many directions, producing a blurred or hazy reflection.

In the case of water reflecting light, it is likely that the reflection is a combination of both specular and diffuse reflection. When the water surface is smooth and still, light is reflected at a specific angle, resulting in a clear and focused reflection.

This is specular reflection. However, when the surface of the water is disturbed, the reflection becomes scattered and blurred, which is characteristic of diffuse reflection.

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To find the wavelength of the wave along the string, we first need to measure the distance between two consecutive points on the wave that are in the same phase.

We can look at the graph provided by the question, whose full cycle of the wave completes in 0.1sec, i.e. demonstrating that this is a complete up and down movement of the point.

As measured in the graph, we see that the distance between two consecutive points is 0.5 cm. Then we calculate the wavelength of the wave using the following formula:

Therefore, the wavelength of the wave corresponds to 0.005m.

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Answer:

Distance from center and mass

Explanation:

Gravity force is determined by the distance from the center of the object, and the mass of the object (so distance and time) speed and acceleration have no effect on the gravity

Answer:

The mass of the object and the distance between objects.

Explanation:

The maximum mass of the plate that can remain glued to the bar can be determined using the maximum force that the glue can withstand.

The wooden bar rotates in a vertical circle around an axis through its center with a constant period of 2.50 seconds. The maximum force that can be exerted on each metal plate is equal to the centrifugal force acting on it due to its rotation around the axis. The centrifugal force is given by the equation Fc = mv^2/r, where Fc is the centrifugal force, m is the mass of the metal plate, v is the velocity of the metal plate, and r is the radius of the circle. In this case, the radius of the circle is equal to half the length of the wooden bar, i.e., r = 0.75 m. The velocity of the metal plate can be calculated from the equation v = 2πr/T, where T is the period of rotation. Substituting the given values, we get: v = (2π)(0.75 m)/(2.50 s) = 4.71 m/s. The maximum force that can be exerted on each metal plate is therefore: Fc = m(4.71 m/s)^2/(0.75 m) = 29.37 mN. To ensure that the maximum force does not exceed 58.0 N, the maximum mass of each metal plate can be calculated by dividing the maximum force by the acceleration due to gravity (9.81 m/s^2): mmax = 58.0 N/(2 × 9.81 m/s^2) = 2.96 kg. Therefore, each metal plate can have a maximum mass of 2.96 kg to avoid exceeding the maximum force that the glue can withstand.

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The weight of a 65 kg person standing on the moon with a mass of 7.348e22 kg and a radius of 1738 km would be approximately 105.3 N.

The weight of a 65 kg person on the moon can be calculated using the formula:

Weight = mass x gravitational acceleration

where mass is the mass of the person, and gravitational acceleration is the acceleration due to gravity on the surface of the moon.

The gravitational acceleration on the surface of the moon is given by:

g = G*M/R^2

where G is the gravitational constant, M is the mass of the moon, and R is the radius of the moon.

In this case, the mass of the moon is M = 7.348e22 kg, and the radius of the moon is R = 1738 km = 1.738e6 m. The gravitational constant is G = 6.6743e-11 Nm^2/kg^2.

So, the gravitational acceleration on the surface of the moon is:

g = G*M/R^2 = (6.6743e-11 Nm^2/kg^2) x (7.348e22 kg) / (1.738e6 m)^2

= 1.62 m/s^2

Now, we can calculate the weight of a 65 kg person on the moon:

Weight = mass x gravitational acceleration

= 65 kg x 1.62 m/s^2

= 105.3 N

Therefore, a 65 kg person would weight about 105.3 N on the surface of the moon.

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The correct option is A. If personal information is accidentally deleted from a computer, The information is backed up, but it is an inferior copy.

Information can be defined as a measure of the degree of uncertainty reduction obtained by receiving a message or measuring a system. It is a fundamental concept in many areas of physics, including thermodynamics, quantum mechanics, and information theory.

In thermodynamics, information is related to the entropy of a system, which quantifies the degree of disorder or randomness. The more information we have about a system, the lower its entropy and the more ordered it becomes.

In quantum mechanics, information is closely related to the concept of entanglement, where two or more particles become so strongly correlated that their states cannot be described independently. The amount of information that can be transmitted through an entangled system is limited by the laws of quantum mechanics.

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Therefore, the mass of ball 2 is approximately 24.7 kg.

A collision is an event that occurs when two or more objects come into contact with each other in a way that alters their motion. In physics, collisions are studied in terms of the conservation of momentum and the conservation of kinetic energy. In an elastic collision, the total kinetic energy of the system is conserved, and the objects bounce off each other without any loss of energy. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound, and the objects may stick together after the collision. Collisions can be categorized into two types: head-on collisions and oblique collisions. In a head-on collision, the objects approach each other directly from opposite directions, while in an oblique collision, the objects approach each other at an angle. Collisions are an important concept in physics and have applications in fields such as engineering, transportation, and sports. Understanding the principles of collisions can help us design safer cars, improve the performance of athletic equipment, and develop new technologies for space exploration.

Here,

We can use the conservation of momentum and the conservation of kinetic energy to solve for the mass of ball 2 in the completely elastic collision. Using the conservation of momentum:

m1v1i + m2v2i = m1v1f + m2v2f

Substituting the known values:

(6.7 kg)(2.0 m/s) + m2(-5.0 m/s) = (6.7 kg)(-6.18 m/s) + m2(0.83 m/s)

Simplifying and solving for m2:

(13.4 - 33.9) kg·m/s = -44.006 kg·m/s + 0.83 m2

-20.5 kg·m/s = 0.83 m2

m2 = (-20.5 kg·m/s) / (0.83 m/s)

m2 ≈ 24.7 kg

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The 0.64 amp current flow  is in a resistor of 227 Ω if the potential difference across the resistor is 145 V.

The sum of the currents flowing through each branch represents the total current in the circuit. By dividing the total current for the circuit by the cell's potential difference, the total resistance for this circuit may be computed.

Using the equation V = E d, determine the potential difference between the two locations. Subtract the current flow rate from the resistance that exists in the circuit. The process of multiplication results in the potential difference, which is measured in volts. This formula, V = I R, is known as Ohm's Law.

The current times the resistance results in the potential difference, also known as voltage. One Joule of energy is produced when one Coulomb of charge moves between two points in a circuit with a potential difference of one Volt.

From ohm's law;

V = IR

Substitute values,

145 = I × 227

I = 0.64 Amp

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The answer is a salt. Salts are ionic compounds that are composed of positively and negatively charged ions.

When dissolved in water, the ions separate and the salt dissolves. Salts also have a high melting point and when heated, they decompose into their constituent elements, producing a flame. This is a chemical property known as thermal decomposition.Thermal decomposition is a type of chemical decomposition induced by the application of heat. It is a specific type of chemical decomposition in which molecules of a compound are broken down into smaller molecules or elements. Thermal decomposition is often used in industry to produce useful chemicals, such as chlorine from table salt, and for the production of metals and alloys from ore.

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Shear stress is tangential tension that results from fluid moving against resistance against a solid surface.  therefore (iii) > (i)  = (ii) option  a).

An item experiences deformation when an exterior force works upon it. if the force's orientation is parallel to the object's surface. Along that line, there will be a distortion. The item in this instance is under tensile or tangential tension.

The stress an object experiences is known as shearing stress or tangential stress when the path of the deforming force or exterior force is parallel to the cross-sectional area.

Shear stress results from forces that are parallel to and reside in the plane of the cross-sectional area, whereas normal stress results from forces that are perpendicular to a cross-sectional area of the substance.

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As the distance between the objects increases, the size of the electric force decreases.

Electricity is a form of energy that results from the movement of charged particles, such as electrons or ions. It is the flow of electric charge through a conductor, which can be used to power devices and machines. Electric phenomena occur naturally, such as in lightning strikes, but can also be harnessed and controlled for practical applications, including lighting, heating, and communication.

Distance refers to the physical length between two points or objects, measured in units such as meters, kilometers, miles, or inches. It is a scalar quantity that only has magnitude and no direction. Distance can be measured using various tools and methods, such as rulers, odometers, or GPS devices.

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The density of water ρ from Table 1 is [tex]1.000 * 10^{3} kg / m^{3}[/tex] . Subbing V and ρ into the expression for mass gives:m=  [tex]V=Ah=(50.0km^{2} )(40.0m)\\=[(50km^{2} ) (\frac{10^{3}m }{1km} )^2] (40.0m) = 2.00 * 10^{9} m^{3}[/tex]

We can ascertain the volume V of the supply from its aspects, and track down the density of water ρ in Table 1. Then, at that point, the mass m can be tracked down in the meaning of density.

[tex]p =\frac{m}{v}[/tex]

Tackling condition ρ = m/V for m gives m=ρV.

The volume V of the supply is its surface region Multiple times its typical profundity h:

[tex]V=Ah=(50.0km^{2} )(40.0m)\\=[(50km^{2} ) (\frac{10^{3}m }{1km} )^2] (40.0m) = 2.00 * 10^{9} m^{3}[/tex]

The density of water ρ from Table 1 is [tex]1.000 * 10^{3} kg / m^{3}[/tex] .

Subbing V and ρ into the expression for mass gives:

[tex]m= (1.00 * 10^3kg / m^3) (2.00* 10^9m^3) \\ = 2.00 * 10^{12} kg[/tex]

An enormous supply contains an extremely huge mass of water. In this model, the heaviness of the water in the repository is mg=1.96× [tex]10^{13}[/tex] N, where g is the speed increase because of the Earth's gravity (around 9.80[tex]m/s^{2}[/tex] ). It is sensible to find out if the dam should supply a power equivalent to this colossal weight. The response is no. As we will find in the accompanying segments, the power the dam should supply can be a lot more modest than the heaviness of the water it keeps down.

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the complete question is:

A reservoir has a surface area of [tex]50.0 km^{2}[/tex] and an average depth of 40.0 m. What mass of water is held behind the dam? (See Figure 2 for a view of a large reservoir—the Three Gorges Dam site on the Yangtze River in central China.)

The minimum antenna length for efficient radiation if it is to be broadcast without the benefit of modulation is 2000 meters and  broadcast after it is amplitude-modulated with a sinusoidal carrier having a frequency that is 100 times the bandwidth of the message signal is 9.87 meters.

To determine the minimum antenna length for efficient radiation, we need to calculate the wavelength of the transmitted signal first.

(a) The given bandwidth of the signal is 30 kHz, which means that the signal occupies a frequency range from f - 15 kHz to f + 15 kHz,

where f is the center frequency of the signal.

Since the signal is broadcast without modulation, its bandwidth is equal to its frequency, so the center frequency is 15 kHz.

The minimum antenna length for efficient radiation is given by: Antenna Length = (1/10) x Wavelength

where Wavelength = Speed of light / Frequency

The speed of light is approximately 3 x 10⁸ meters per second.

Therefore, the wavelength of the signal is:

Wavelength = Speed of light / Frequency = 3 x 10⁸ / 15,000 = 20,000 meters

The minimum antenna length for efficient radiation is then:

Antenna Length = (1/10) x Wavelength = (1/10) x 20,000 = 2000 meters

Therefore, the minimum antenna length for efficient radiation without modulation is 2000 meters.

(b) The message signal is amplitude-modulated with a sinusoidal carrier having a frequency that is 100 times the bandwidth of the message signal.

This means that the carrier frequency is 100 x 30 kHz = 3 MHz.

The bandwidth of the transmitted signal is then the sum of the carrier frequency and the message signal bandwidth, which is 3 MHz + 30 kHz = 3.03 MHz.

Using the same formula as in part (a), we can calculate the wavelength of the transmitted signal:

Wavelength = Speed of light / Frequency = 3 x 10⁸ / 3.03 x 10⁶ = 98.68 meters

The minimum antenna length for efficient radiation is then:

Antenna Length = (1/10) x Wavelength = (1/10) x 98.68 = 9.87 meters

Therefore, the minimum antenna length for efficient radiation after modulation with a sinusoidal carrier is 9.87 meters.

The minimum antenna length for efficient radiation without modulation is 2000 meters and  the minimum antenna length for efficient radiation after modulation with a sinusoidal carrier is 9.87 meters.

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Answer:

The person sings at the same frequency as the piano wire, called the resonance frequency.

Explanation:

The person sings at a different frequency than the piano wire, called as resonance frequency. So, option d is correct.

Interference directs to a phenomenon in which two wires meet while traveling along the exact medium and they superpose to create a resulting wave that is lower, greater, or the same amplitude as each other. The soundboard is a big wooden panel that amplifies the sound of the vibrating string.

In the given scenario, a beat frequency is listened to by a player when using a tuning fork to adjust a piano wire. Thus, the piano tuner should change the strain in the wire, this decreases the frequency of the wire.

For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.

Q = It, where I is the current, t is the time, and Q is the total charge.

Q = N

N is the quantity of electrons.

The two equations together give us:

Ne = It,

To solve for t, we obtain:

t = Ne/I

Inputting the values provided yields:

t = (3.00× [tex]10^{20}[/tex])

(1.60× [tex]10^{-19}[/tex] C/e) / (80.0× [tex]10^{-3}[/tex] A)

t = 6.00× [tex]10^{14}[/tex] s

For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.

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Answer:

all of these

Explanation:

D. all of these is the correct answer

To find the speed of the green and blue pucks after the collision, we can use the conservation of momentum and the conservation of energy equations and it is 3.33 m/s and  2.78 m/s respectively.

First, let's find the mass of the blue puck. If the mass of the blue puck is 20% greater than the mass of the green one, then:

m (blue) = 1.2 * m (green)

Next, let's use the conservation of momentum equation:

m (green) * v (green), initial + m (blue) * v (blue), initial = m (green) * v (green), final + m (blue) * v (blue), final

Since the pucks approach each other with equal and opposite momenta, we can set v (blue), initial = -v (green), initial = -10 m/s. Plugging in the values we know:

m (green) * 10 + 1.2 * m (green) * (-10) = m (green) * v (green), final + 1.2 * m (green) * v (blue), final

Next, let's use the conservation of energy equation. If half the kinetic energy is lost during the collision, then:

0.5 * m (green) * v (green), initial2 + 0.5 * m (blue) * v (blue), initial2 = 0.5 * (m (green) * v (green), final2 + m (blue) * v (blue), final2)

Plugging in the values we know:

0.5 * m (green) * 102 + 0.5 * 1.2 * m (green) * (-10)2 = 0.5 * (m (green) * v (green), final2 + 1.2 * m (green) * v (blue), final2)

Now we can solve for the final velocities of the pucks using these two equations. We get:

v (green), final = -3.33 m/s
v (blue), final = 2.78 m/s

Therefore, the speed of the green puck after the collision is 3.33 m/s and the speed of the blue puck after the collision is 2.78 m/s.

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The required wavelength is calculated to be 715 nm and it belongs to infrared region.  

The band-gap of the semiconductor cdse is given as 1.74 ev.

The equation of Planck is mathematically written as,

E = h c /λ

where,

h is planck's constant

c is speed of light

λ is wavelength

E is energy/band-gap

Converting electron volts to joules we should multiply by 1.6 × 10⁻¹⁹ J

Putting all the known values and making wavelength as subject,

λ = h c /E = (6.626 × 10⁻³⁴× 3 ×10⁸)/(1.74× 1.6 × 10⁻¹⁹) = (19.88 × 10⁻²⁶)/(2.78× 10⁻¹⁹) = 7.15 × 10⁻⁷ m = 715 × 10⁻⁹ m = 715 nm

By looking into the wavelengths of electromagnetic spectrum, we can say that this wavelength belongs to infrared.

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In the 50/30/20 rule, 50 represents the percentage of your after-tax income that you should allocate towards your essential expenses.

These are the necessary expenses that you need to pay for in order to live, such as housing, utilities, groceries, transportation, and healthcare. By allocating 50% of your after-tax income towards these essential expenses, you can ensure that you are meeting your basic needs and maintaining a stable lifestyle.

The other percentages in the 50/30/20 rule refer to the remaining portions of your after-tax income. 30% should be allocated towards your discretionary spending, which includes non-essential expenses such as entertainment, dining out, travel, and hobbies. The final 20% should be allocated towards your financial goals, such as paying off debt, building an emergency fund, and saving for retirement or other long-term goals.

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Answer:

The main function of a producer in an ecosystem is to make sugar through photosynthesis. Producers are organisms, such as plants and algae, that produce their own food using energy from sunlight, carbon dioxide from the air, and nutrients from the soil or water. Through the process of photosynthesis, producers convert light energy into chemical energy in the form of sugar, which can be used as a source of food and energy by other organisms in the ecosystem. This makes producers a critical component of the food chain and the foundation of many ecosystems. Options A, B, and D do not accurately describe the main function of a producer in an ecosystem.

mass of dog and boat are m = 4.5 kg, and M = 18 kg respectively.

Initial distance of dog from the shore, D = 4.5 m

Figure 1 shows a 5.4 N force pushing two gliders along an air track. The 160 g spring between the gliders is compressed. The spring is firmly attached to the gliders and does not sag. This situation demonstrates Hooke’s Law, which states that the force required to compress a spring is directly proportional to the amount of displacement of the spring. In this case, the 5.4 N force is pushing the gliders towards each other, compressing the spring and causing a displacement. As Hooke's Law states, the greater the force used to compress the spring, the greater the displacement will be.

The stiffness of the spring in this situation would be determined by the spring constant, which can be calculated using the formula F = -kx. The spring constant can be calculated by using the displacement of the spring.

When the 5.4 N force is applied, the kinetic energy of the gliders is converted into potential energy, which is stored in the compressed spring. When the force is removed, the potential energy is converted back into kinetic energy and the gliders move away from each other.

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The toy car is moving at a speed of approximately 5.74 m/s after it has been pushed for a distance of 2 meters.

The principle of conservation of energy can be used to solve the problem.

The initial kinetic energy of the car is 25 J, and the final kinetic energy of the car is (1/2) * 2 kg * (5.74 m/s)^2, which is approximately 40.97 J.

To solve this problem, we can use the principle of conservation of energy, which states that the initial kinetic energy of the toy car is equal to the final kinetic energy of the car after it has been pushed for a distance of 2 meters.

The initial kinetic energy of the car is given by:

KE1 = (1/2) * m * v1^2

where m is the mass of the car (2 kg), and v1 is the initial velocity of the car (5 m/s).

KE1 = (1/2) * 2 kg * (5 m/s)^2

KE1 = 25 J

The final kinetic energy of the car is given by:

KE2 = (1/2) * m * v2^2

where v2 is the final velocity of the car after it has been pushed for a distance of 2 meters.

Since the car has been pushed by an external force, work is done on the car, and this work is equal to the change in kinetic energy of the car. The work done on the car is given by:

W = F * d

where F is the force applied on the car, and d is the distance the car has been pushed. Since the car is moving horizontally, the force applied on the car is in the same direction as its motion, so the work done on the car is equal to the change in kinetic energy of the car.

W = KE2 - KE1

Substituting the values we get:

W = (1/2) * 2 kg * v2^2 - 25 J

W = (1/2) * 2 kg * v2^2 - 25 J = F * d = (2 kg * a) * 2 m = 4 kg m/s^2 * 2 m = 8 J

Solving for v2 we have:

v2 = sqrt((2 * (W + KE1)) / m)

v2 = sqrt((2 * (8 J + 25 J)) / 2 kg)

v2 = sqrt(66 J / 2 kg)

v2 = sqrt(33) m/s

Therefore, the toy car is moving at a speed of approximately 5.74 m/s after it has been pushed for a distance of 2 meters.

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The formula for the frequency observed by the observer when both the source and the observer are moving toward each other is given by:

f' = f0 (v + vo)/(v + vs)

where f0 is the frequency of the source, v is the speed of sound in the medium of the source, vs is the speed of sound in the medium of the observer, vo is the speed of the observer, and f' is the apparent frequency observed by the observer.

The formula for the wavelength of a wave is :

λ = v/f

where λ is the wavelength, v is the speed of the wave, and f is the frequency.

the speed of sound is different in the two media, and the wavelength of the sound wave will also be different in the two media. Let λ0 be the wavelength of the sound wave in the medium of the source and λ be the wavelength observed by the observer.

but this, we have:

λ = v'/f'

where v' is the relative speed of the source and the observer.

Since both the source and the observer are moving towards each other, their relative speed is:

v' = v + vs + vo

Substituting the given values, we get:

f' = f0 (v + vo)/(v + 2v)

= f0 (1 + vo/v)/3

λ0 = v/f0

λ = v' / f'

= (v + vs + vo) / [f0 (1 + vo/v)/3]

= 3(v + vs + vo) λ0/(1 + vo/v)

solving this, we get:

λ = 3(v + 2V)λ0/(1 + v0/v)

Thus, the apparent wavelength seen by the observer is

3(v + 2V)λ0/(1 + v0/v).

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Question

A coconut of mass m falls from its tree through a vertical distance of s and could reach ground with a velocity of v ms−1 due to air resistance. The work done by air resistance is:

A.) −m/2 (2gs−v2)

B.) −1/2 mv^2

C.) −mgs

D.) mv^2+2mgs

Solution

Correct option is A)

Here, a coconut of mass m falls from its tree through a vertical distance of s, with a velocity of v hence work done by gravity is,

Wg=mgs .......(1)

Change in velocity of coconut is,

E=1/2m(u−v)^2 = −1/2m(v)2 ........(2)

Now, total work done on coconut is equal to change in kinetic energy hence,

Wa+Wg=1/2mv^2

where, Wa is  work done by air resistance.

Using (1) and (2), we get

Wa=1/2mv^2−Wg

Wa=1/2mv^2−mgs

Wa=−m/2(2gs−v2)

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