May
SHOW YOUR WORK IN ALL QUESTIONS. Acceleration due to gravity: a = 9.81 m/s2
1.) (a) A ball is dropped from 4 meters above the ground. If it begins at rest, how long does it take
to hit the ground?
(b) A ball is thrown upward at 4 meters per second starting from ground level. How long does it
take for the ball to return to the ground?
(c) If a ball that is 4 meters above the ground is thrown horizontally at 4 meters per second,
how long will it take for the ball to hit the ground?
(d) In question (c) above, how far will the ball travel in the horizontal direction before it hits th
ground?
(e) Drop a ball from a height of 2 meters and, using a stopwatch, record the time it takes to
reach the ground. Repeat this two more times and record all the times in the table belov-
then find the average time. Be sure to release the ball from rest rather than throwing it
or down.
Test Number
Time (seconds)​

Answer:

I believe it’s A

Explanation:

Answer:

A is correct (1 nm to 100 nm)

Explanation:

I just took the exam

Answer:

SEE EXPLANATION

Explanation:

The dimensional formula of gravitational constant is given by,

M^-1 L^3 T^-2  

Where,  

M = Mass

L = Length

T = Time

Dimensional formula of Specific Heat Capacity =[ M^0L^2T^-2K^-1]

Answer:

Explanation:

Given that:

the initial angular velocity [tex]\omega_o = 0[/tex]

angular acceleration [tex]\alpha[/tex] = 4.44 rad/s²

Using the formula:

[tex]\omega = \omega_o+ \alpha t[/tex]

Making t the subject of the formula:

[tex]t= \dfrac{\omega- \omega_o}{ \alpha }[/tex]

where;

[tex]\omega = 1.53 \ rad/s^2[/tex]

∴

[tex]t= \dfrac{1.53-0}{4.44 }[/tex]

t = 0.345 s

b)

Using the formula:

[tex]\omega ^2 = \omega _o^2 + 2 \alpha \theta[/tex]

here;

[tex]\theta[/tex] = angular displacement

∴

[tex]\theta = \dfrac{\omega^2 - \omega_o^2}{2 \alpha }[/tex]

[tex]\theta = \dfrac{(1.53)^2 -0^2}{2 (4.44) }[/tex]

[tex]\theta =0.264 \ rad[/tex]

Recall that:

2π rad = 1 revolution

Then;

0.264 rad = (x) revolution

[tex]x = \dfrac{0.264 \times 1}{2 \pi}[/tex]

x = 0.042 revolutions

c)

Here; force = 270 N

radius = 1.20 m

The torque = F * r

[tex]\tau = 270 \times 1.20 \\ \\ \tau = 324 \ Nm[/tex]

However;

From the moment of inertia;

[tex]Torque( \tau) = I \alpha \\ \\ Since( I \alpha) = 324 \ Nm. \\ \\ Then; \\ \\ \alpha= \dfrac{324}{I}[/tex]

given that;

I = 84.4 kg.m²

[tex]\alpha= \dfrac{324}{84.4} \\ \\ \alpha=3.84 \ rad/s^2[/tex]

For re-tardation; [tex]\alpha=-3.84 \ rad/s^2[/tex]

Using the equation

[tex]t= \dfrac{\omega- \omega_o}{ \alpha }[/tex]

[tex]t= \dfrac{0-1.53}{ -3.84 }[/tex]

[tex]t= \dfrac{1.53}{ 3.84 }[/tex]

t = 0.398s

The required time it takes= 0.398s

Answer:

Power lines

Explanation:

Generators induce that current that runs the turbines

Turbines also induce currents from water waves that is transmitted.

Transformers change A.C to D.C or vice versa.

Answer: [tex]65.9^{\circ}[/tex]

Explanation:

Given

Intensity must be reduced by a factor of 6

Intensity is given by [tex]I=I_o\cos ^2\theta\\[/tex]

Substitute [tex]I[/tex] by [tex]\frac{I_o}{6}[/tex]

[tex]\Rightarrow \dfrac{I_o}{6}=I_o\cos ^2\theta\\\\\Rightarrow \cos^2\theta =\dfrac{1}{6}\\\\\Rightarrow \cos \theta=\dfrac{1}{\sqrt{6}}\\\\\Rightarrow \theta=65.9^{\circ}[/tex]

So, the disk must be rotated by an angle of [tex]65.9^{\circ}[/tex] .

Answer:

a) the period of vibration of the bird’s wings is 0.0667s

b) the frequency of the wings’ vibration is 15 Hz

c) the angular frequency of the bird’s wingbeats is 94.2 rad/s

Explanation:

Given the data in the question;

beat at a rate of up to 900 times per minute.

The number of vibrations per unit time can be be determined as follows;

frequency f = number of vibration / time ---------- let this be equation 1

Also Time period T is;

T = 1/f { time period and frequency are reciprocal to each other }

T = 1/f ---------- Let this be equation 2

Then, the angular frequency ω can be determined using the formular;

ω = 2π × f -------------- Let this be equation 3.

Now, given that; The wings of the blue-throated hummingbird beat at a rate of up to 900 times per minute; Hence,

from equation 1, frequency f = number of vibration / time

f = 900 / 1 min

f = 900 / 60 sec

f = 15 Hz

Therefore, the frequency of the wings’ vibration is 15 Hz

a) the period of vibration of the bird’s wings

from equation 2, T = 1/f ,

we substitute in the value of f

T = 1 / 15 Hz

T = 0.0667s

Therefore, the period of vibration of the bird’s wings is 0.0667s

c) the angular frequency of the bird’s wingbeats;

from equation 3, ω = 2π × f

we substitute

ω = 2π × 15 Hz

ω = 94.2 rad/s

Therefore, the angular frequency of the bird’s wingbeats is 94.2 rad/s

Solution :

Given data:

Area of the solar sail, A = 16 [tex]$m^2$[/tex]

Mass (array + sail), m = [tex]$3 \times 10^{-3}$[/tex] kg

Power, P = 100 GW

               = [tex]$10^{11}$[/tex] W

Time, t = 10 min

           = 10 x  60 s

Distance, D = [tex]$4.3 \times 4 \times 10^{16}$[/tex] m

Kinetic energy, [tex]$KE=\frac{1}{2}mv^2=P\times t$[/tex]

[tex]$v=\sqrt{\frac{2Pt}{m}}$[/tex]

[tex]$v=\sqrt{\frac{2\times 10^{11}\times 600}{3 \times 10^{-3}}}$[/tex]

  [tex]$=2 \times 10^8$[/tex] m/s

So, the acceleration is [tex]$a=\frac{v}{t}$[/tex]

[tex]$a=\frac{2 \times 10^8}{6 \times 10^2} \ m/s^2$[/tex]

 [tex]$=333333.33 \ m/s^2$[/tex]

Therefore, force,

[tex]$F = ma$[/tex]

   [tex]$=3 \times 10^{-3}\times 333333.33$[/tex]

   = 1000 N

Pressure, [tex]$P=\frac{F}{A}$[/tex]

                   [tex]$=\frac{1000}{16}$[/tex]

                   [tex]$=62.5 \ N/m^2$[/tex]

Therefore, time taken is t

Now the distance is

[tex]$d_1=\frac{1}{2}at_1^2$[/tex]

[tex]$d_1=0.5 \times 333333.33 \times (600)^2$[/tex]

    [tex]$=6 \times 10^{10} \ m$[/tex]

Now, the distance, [tex]$d_2 = D-d_1=v.t_2$[/tex]

Now, [tex]$t_2=\frac{(17.2 \times 10^{16})-(6 \times 10^{10})}{2 \times 10^8}$[/tex]

            = 859999700 s

Therefore, total time is

[tex]$T=t_1+t_2$[/tex]

  = 86000300 s

  = 27.27 years

Answer:

1. Laod = 500 N

2. Effort = 250 N

Explanation:

From the question given above, the following data were obtained:

Input work = 187.5 J

Output work = 125 J

Load distance = 25 cm

Effort distance = 75 cm

1. Determination of the load.

Output work = 125 J

Load distance = 25 cm = 25/100 = 0.25 m

Load =?

Output work = Load × Load distance

125 = Load × 0.25

Divide both side by 0.25

Load = 125 / 0.25

Laod = 500 N

2. Determination of the effort.

Input work = 187.5 J

Effort distance = 75 cm = 75/100 = 0.75 m

Effort =?

Input work = Effort × Effort distance

187.5 = Effort × 0.75

Divide both side by 0.75

Effort = 187.5 / 0.75

Effort = 250 N

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark, get ready, start.

A significant negative environmental impact of using nuclear fuel is mining. The correct option is b.

Mining is the process or industry of obtaining coal or other minerals from a mine.

Using nuclear fuels for mining will have no negative impact on the environment. All other terms represent negative impact of nuclear fuel Thus,  The correct option is b.

Learn more about mining.

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Answer:

201.8 days

Explanation:

The activity of a radioactive sample as a function of times is :

[tex]$R=R_0e^{\frac{0.693t}{T_{1/2}}}$[/tex]

Here, [tex]$R_0$[/tex] = the initial activity

          [tex]$T_{1/2}$[/tex] = half life

          t = elapsed time

Now rearranging the equation for time, t, we get:

[tex]$\frac{R}{R_0}=e^{-\frac{0.693t}{T_{1/2}}}$[/tex]

[tex]$\ln\left(\frac{R}{R_0}\right)=-\frac{0.693t}{T_{1/2}}$[/tex]

[tex]$t=\frac{-\ln\left(\frac{R}{R_0}\right)T_{1/2}}{0.693}$[/tex]

[tex]$t=\frac{-\ln\left(\frac{25}{350}\right)\times 53}{0.693}$[/tex]

 = 201.8 days

Therefore, the required time is 201.8 days

Answer:

No, it does not.

Explanation:

According to the Law of Gravitation, something going down has more kinetic energy than something going up because it attracts pressure from around it when going down. When it goes up, it has less gravitational force and inertia also stops the ball from rolling upward. Therefore, without the amount of kinetic energy, it will not have the same amount of acceleration.

Answer:

Movement of Electrons in opposite direction of the rotation of the pickup coil leads to the direction of Electrical energy ( Alternating current ).

Explanation:

For a Generator to generate electricity, Electrons that is found in the rotating coil of the Generator will experience some sort of force that makes them to start moving in a direction that is perpendicular to the direction of the rotating/pickup coil found in the Generator.

The conversion of mechanical energy (Rotation of the pickup coil ) to electrical energy takes place in the Generator

The generator makes an alternating current because electrons move in opposite direction of the rotating coil

In other to generate a Direct current using a generator we have to replace the slip rings with commutator.

Answer: 50 km, 0, 27.78 m/s

Explanation:

Given

Circumference of the track is [tex]12.5\ km[/tex]

Speed of car is [tex]100\ km/h[/tex]

Car drives for [tex]30\ \text{minute}\ or\ 0.5\ hr[/tex]

(a)Distance traveled is

[tex]\Rightarrow D=100\times 0.5\\\Rightarrow D=50\ km[/tex]

(b)displacement of the car

It can be observed that 12.5 is a multiple of 50, that is, 50 km can be interpreted as 4 complete rounds of the track.

Therefore, the displacement of the car is zero.

(c)To convert kmph to m/s, multiply the entity by [tex]\frac{5}{18}[/tex]

[tex]\Rightarrow 100\times \dfrac{5}{18}\\\\\Rightarrow 27.78\ m/s[/tex]

Answer:

65 Newtons

Explanation:

A book is kept on the table. The book is applying 65 N of force down on the table. So the table will also apply 65 N force to the book.

According to physics, a force is an effect that has the power to change an object's motion. A force can cause a massed item to accelerate or modify its velocity. A push or a pull is a straightforward method to explain force. Considering that a force has both a magnitude and a direction, it is a vector quantity.

The pace at which an object's direction changes when it is traveling is referred to as its velocity, and is measured by a particular unit of time and from a particular point of view.

When the book is applying force on the table that is mg, and it is 65 N the table will also generate a normal reaction force which will be equal to the force applied by the book which is 65 N.

To get more information about Force :

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Answer:

Answer:

The beta ray Energy (E) absorbed = 0.009105 Joules

Explanation:

The absorbed dose rate in the tissue can be determined by using the known formula:

Dose equivalent = absorbed dose × relative biological effective (RBE)

[tex]absorbed \ dose = \dfrac{Dose \ equivalent}{RBE}[/tex]

[tex]absorbed \ dose = \dfrac{17 \times 10^{-3} \ rem}{1.4}[/tex]

absorbed dose = 12.14 × 10⁻³ rad

absorbed dose = 12.14 m rad

However, since the absorbed dose is determined, the energy absorbed in one year is can be expressed as:

Energy (E) = mass × absorbed rate

Energy (E) = 75 kg × 12.14 × 10⁻³ rad

Energy (E) = 75 kg × 12.14 × 10⁻³× 10⁻² J/kg

Energy (E) = 75 × 12.14 × 10⁻³× 10⁻² Joules

Energy (E) = 0.009105 Joules

Answer:

In the morning the molecules were moving away from each other with a smaller speed than when the truck was carrying the substance.

Explanation:

Answer:

Explanation:

The most likely thing that would happen is that the galaxies continue becoming more and more massive, eventually becoming part of a galaxy cluster. These are massive but cluttered parts of the universe that hold many galaxies extremely close to one another. This also leads to galaxies colliding with one another, although when this happens they usually seem to pass right through each other as if they were ghosts. This is simply due to their sheer size and distance between their bodies of mass.

Answer:

It will merge with other galaxies

Explanation:

Pearson Connexus 2023

Answer:

The magnitude of the free-fall acceleration at the orbit of the Moon is [tex]2.728\times 10^{-3}\,\frac{m}{s^{2}}[/tex] ([tex]\frac{2.784}{10000}\cdot g[/tex], where [tex]g = 9.8\,\frac{m}{s^{2}}[/tex]).

Explanation:

According to the Newton's Law of Gravitation, free fall acceleration ([tex]g[/tex]), in meters per square second, is directly proportional to the mass of the Earth ([tex]M[/tex]), in kilograms, and inversely proportional to the distance from the center of the Earth ([tex]r[/tex]), in meters:

[tex]g = \frac{G\cdot M}{r^{2}}[/tex] (1)

Where:

[tex]G[/tex] - Gravitational constant, in cubic meters per kilogram-square second.

[tex]M[/tex] - Mass of the Earth, in kilograms.

[tex]r[/tex] - Distance from the center of the Earth, in meters.

If we know that [tex]G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}[/tex], [tex]M = 5.972\times 10^{24}\,kg[/tex] and [tex]r = 382.26\times 10^{6}\,m[/tex], then the free-fall acceleration at the orbit of the Moon is:

[tex]g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (5.972\times 10^{24}\,kg)}{(382.26\times 10^{6}\,m)^{2}}[/tex]

[tex]g = 2.728\times 10^{-3}\,\frac{m}{s^{2}}[/tex]

Answer:

6 W

Explanation:

From the given information:

The resistance in Parallel for 2R is:

[tex]R_p = \dfrac{2R\times 2R}{2R+2R} \\ \\ R_p= R[/tex]

The equivalent resistance:

[tex]R_{eq} = R_p + R = 2R[/tex]

[tex]R_{eq} = 2(3)[/tex]

[tex]R_{eq} = 6 \ \ ohms[/tex]

The current through the circuit in R is:

[tex]= \dfrac{12}{R+R} \\ \\ = \dfrac{12}{2\times 3} \\ \\ = 2 A[/tex]

The current through the circuit in 2R is:

[tex]I_2R = (2A) \times \dfrac{2R}{2R+2R}[/tex]

[tex]I_2R = 2A \times \dfrac{1}{2} \\ \\ I_2R = 1A[/tex]

Finally, the thermal energy:

[tex]P_{2R} = (1)^2 (2R)[/tex]

[tex]P_{2R} = (1)^2 (2\times 3)[/tex]

[tex]P_{2R} = 6W[/tex]

Answer:

d = 1.51 x 10⁻⁵ m = 15.1 μm

Explanation:

We will use young's Double Slit formula here:

[tex]Y = \frac{\lambda L}{d}\\\\d = \frac{\lambda L}{Y}[/tex]

where,

d = width of strand = ?

λ = wavelength = 631.8 nm = 6.318 x 10⁻⁷ m

L = Screen to hair distance = 1.2 m

Y = fringe spacing = 5.02 cm = 0.0502 m

Therefore,

[tex]d = \frac{(6.318\ x\ 10^{-7}\ m)(1.2\ m)}{0.0502\ m}[/tex]

d = 1.51 x 10⁻⁵ m = 15.1 μm

Answer:

Heat transfer is an engineering discipline that concerns the generation, use, conversion, and exchange of heat (thermal energy) between physical systems.

Explanation:

Answer:

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.

Explanation:

hope that helps

Answer:

x = 4 m

Explanation:

For this exercise we must use the rotational equilibrium relationship, where we place zero at the turning point and counterclockwise rotations we will consider positive

as it indicates that the bar is in equilibrium, its center of mass coincides with the turning point, so the distance is zero and does not create torque on the system

        ∑τ  = 0

        W 3 - w x = 0

        x = 3W / w

        x = 3 Mg / mg

        x = 3 M / m

let's calculate

       x = 3 60/45

       x = 4 m

Answer:

1. 10 ft/s² straight up

2. 4 Km north-west

3. 20 m/s South

Explanation:

To successfully categorize the quantities given above as vectors, we must understand what vector quantity is.

A vector quantity is a quantity that has both magnitude and direction.

Considering the question given above, the vector quantities are:

1. 10 ft/s² straight up

2. 4 Km north-west

3. 20 m/s South

The remaining quantities in the question are not considered as vectors because they only have magnitude but no direction. They are therefore referred to as scalar quantities.

Answer:

The unknown substance is Aluminum.

Explanation:

We'll begin by calculating the change in the temperature of substance. This can be obtained as follow:

Initial temperature (T₁) = 25 ⁰C

Final temperature (T₂) = 100 ⁰C

Change in temperature (ΔT) =?

ΔT = T₂ – T₁

ΔT = 100 – 25

ΔT = 75 ⁰C

Finally, we shall determine the specific heat capacity of the substance. This can be obtained as follow:

Change in temperature (ΔT) = 75 ⁰C

Mass of the substance (M) = 135 g

Heat (Q) gained = 9133 J

Specific heat capacity (C) of substance =?

Q = MCΔT

9133 = 135 × C × 75

9133 = 10125 × C

Divide both side by 10125

C = 9133 / 10125

C = 0.902 J/gºC

Thus, the specific heat capacity of substance is 0.902 J/gºC

Comparing the specific heat capacity (i.e 0.902 J/gºC) of substance to those given in the table above, we can see clearly that the unknown substance is aluminum.

Answer:

r = 1.07 m

Explanation:

The maximum radius of the propeller that can be allowed is given by the following formula:

[tex]v = r\omega\\\\r = \frac{v}{\omega}[/tex]

where,

r = maximum possible radius of the propeller = ?

v = maximum possible linear speed of the propeller = 270 m/s

ω = angular speed of the propeller = (2400 rpm)(2π rad/1 rev)(1 min/60 s)

ω = 251.33 rad/s

Therefore,

[tex]r = \frac{270\ m/s}{251.33\ rad/s}[/tex]

r = 1.07 m