Calculate the height that the ball bounces.
Sketch the position-time graph for the motion of the ball during the 2,89 s.
(Use the ground as zero position)
Show the following on the graph:
The position of the ball at 0 s.
The position of the ball at 0,5 s.
The position of the ball at time ty. how the graph will be? ​

Answers

Answer 1

Answer:

im bouta get 50 points

Explanation:


Related Questions

Por que nos dias de hoje o futebol é mais técnico, com mas estratégias e mais disputado?

Answers

Explanation:

[tex]which \: language \: is \: this[/tex]

[tex]pls \: write \: in \: english[/tex]

[tex]then \: only \: i \: can \: answer \: u[/tex]

[tex]otherwise \: sry[/tex]

A helicopter is ascending vertically witha speed of 5.40 m/s. At a height of 105 m above the earth a package is dropped from the helicopter. How much time does is take for the package to reach the ground

Answers

Answer: 5.21 s

Explanation:

Given

Helicopter ascends vertically with [tex]u=5.4\ m/s[/tex]

Height of helicopter [tex]h=105\ m[/tex]

When the package leaves the helicopter, it will have the same vertical velocity

Using equation of motion

[tex]\Rightarrow h=ut+\dfrac{1}{2}at^2\\\\\Rightarrow 105=-5.4t+0.5\times 9.8t^2\\\Rightarrow 4.9t^2-5.4t-105=0\\\\\Rightarrow t=\dfrac{5.4\pm \sqrt{5.4^2+4\times 4.9\times 105}}{2\times 4.9}\\\\\Rightarrow t=\dfrac{5.4\pm 45.68}{9.8}\\\\\Rightarrow t=5.21\ s\quad \text{Neglect negative value}[/tex]

So, package will take 5.21 s to reach the ground

1000 grams of water is heated from 0 degree to 200 degree . The specific heat of water is 4186 j/kg.°C. Estimate the change in entropy of the water.​

Answers

Answer:2

Explanation:

In the following circuit (Fig.3), calculate the intensity I through the resistance 3 using the principle of superposition.

Answers

Answer:

time

Explanation:

A wave has angular velocity 12 rad/sec and maximum displacement X cm (X= last two digit [1] of your student’s ID). Calculate the maximum acceleration of the wave.

Answers

Answer:

[tex]a=1440\ m/s^2[/tex]

Explanation:

Given that,

The angular velocity of a wave, [tex]\omega=12\ rad/s[/tex]

The maximum displacement of the wave, A = 10 cm (let)

The maximum acceleration of the wave is given by :

[tex]a=-A\omega^2[/tex]

Put all the values,

[tex]a=10\times 12^2\\\\a=1440\ m/s^2[/tex]

So, the maximum acceleration of the wave is equal to [tex]1440\ m/s^2[/tex].

Wind is caused by ___. the earth's tilt the Coriolis effect temperature differences humidity

Answers

I am guessing wind is caused by climate change in the atmosphere

Explanation:

wind is cause by climate change in the atmosphere that depends weather is is breezy really cold or rain and cold

Answer:

caused by the uneven heating of the Earth by the sun and the  own rotation.

13. How many electrons does a complete third electron shell hold?

Answers

Answer:

A) 8

A complete third electron shell holds 8 electrons

---------------------------

hope it helps...

have a great day!!

Answer:

8

Explanation:

A parallel-plate capacitor is connected to a battery of electric potential difference V. If the plate separation is decreased, do the following quantities increase, decrease, or remain the same: (a) the capacitor’s capacitance, (b) the potential difference across the capacitor, (c) the charge on the capacitor, (d) the energy stored by the capacitor, (e) the magnitude of the electric field between the plates, and (f ) the energy density of that electric field?

Answers

Answer:

a) increases.

b) remains the same.

c) increases.

d) increases.

e) increases.

f) increases.

Explanation:

a)

Since the capacitance of a parallel-plate  depends only on geometric constants and the dielectric between the plates, we can use the following expression to asess the value of the capacitance:

       [tex]C = \epsilon_{0}*\frac{A}{d} (1)[/tex]

       where ε₀ = permitivitty of  free space

                   A = area of one of the plates

                   d=  plate separation

As we can see, if the plate separation is decreased, the value of the capacitance must increase.

b)  

Per definition the capacitance explains the relationship between the charge on one of the conductors, and the potential difference between them, as follows:

        [tex]C = \frac{Q}{V} (2)[/tex]

Assuming that the capacitor remains connected to the battery when the plate separation is decreased, since the voltage can't change (as it must hold the same voltage than previously since it's directly connected to the battery) the potential difference between plates must remain the same.

c)

From B, we know that V in (2) must remain constant. Since we know from (1) that C must increase, this means from (2) that Q must increase too.

d)

The energy stored in the electric field between the plates can be expressed as follows in terms of the capacitance C and the potential difference V:

       [tex]U = \frac{1}{2}* C*V^{2} (3)[/tex]

From (1) in a) and from b) we know that the capacitance C must increase whilst V must remain the same, so U in (3) must increase also.

e)

In the capacitor the magnitude of the Electric field between the plates is constant, and is related to the potential difference between them by the following linear relationship:

       [tex]V = E*d (4)[/tex]

Since we know that V must remain the same, if the distance d decreases, the electris field E must increase in the same ratio in order to keep the equation balanced.

f)

The energy density of the electric field is defined as the energy stored between plates by unit volume, as follows:

       [tex]u = \frac{U}{v} = \frac{\frac{1}{2}* C*V^{2}}{A*d} =\frac{1}{2}* \epsilon_{0}*\frac{A*V^{2} }{A*d*d} = \frac{1}{2} *\epsilon_{0}*E^{2} (5)[/tex]

Since it's proportional to the square of  the electric field, and we know from e) that the magnitude of the electric field must increase, u must increase too.

what change occurs to the mass of an object when a unbalanced

Answers

Answer:

The mass decreases

Explanation:

Just smart

ou charge a piece of aluminum foil (mass = 4.99 g) by touching it to a charged rod. The charged rod gives the aluminum foil a charge of 13 µC. Your professor brings a charged plate over and tells you to put the aluminum foil on top of the plate. To your surprise the aluminum foil hovers motionless in the air above it! Calculate the value of the electric field from the charged plate (assume it is a uniform field and the aluminum foil is a point charge).

Answers

Answer:

The appropriate answer is "3761.69 N/C".

Explanation:

Given that:

Mass,

m = 4.99 g

or,

   = [tex]4.99\times 10^{-3} \ kg[/tex]

Charge,

q = 13 µC

or,

  = [tex]13\times 10^{-6} \ C[/tex]

As we know,

⇒ [tex]F=mg=Eq[/tex]

then,

⇒ [tex]E=\frac{mg}{q}[/tex]

By putting the values, we get

        [tex]=\frac{4.99\times 10^{-3}\times 9.8}{13\times 10^{-6}}[/tex]

        [tex]=3761.69 \ N/C[/tex]

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping

Answers

Explanation:

The centripetal force [tex]F_c[/tex] on the car must equal the frictional force f in order to avoid slipping off the road. Let's apply Newton's 2nd law to the y- and x-axes.

[tex]y:\:\:\:\:N - mg = 0[/tex]

[tex]x:\:\:F_c = f \Rightarrow \:\:\:m \dfrac{v^2}{r} = \mu N[/tex]

or

[tex]m \dfrac{v^2}{r} = \mu mg[/tex]

Solving for [tex]\mu[/tex],

[tex]\mu = \dfrac{v^2}{gr} = \dfrac{(12.0\:\frac{m}{s})^2}{(9.8\:\frac{m}{s^2})(52\:m)} = 0.28[/tex]

A child throws a ball vertically upward to a friend on a balcony 28 m above him. The friend misses the ball on its upward flight but catches it as it is falling back to earth. If the friend catches the ball 3.0 s after it is thrown, at what time did it pass him on its upward flight

Answers

Answer:

[tex]t=1.9 sec[/tex]

Explanation:

From the question we are told that:

Height [tex]h=28m[/tex]

Time [tex]t=3s[/tex]

Generally the Newton's equation for Initial velocity upward is mathematically given by

 [tex]s=ut+\frtac{1}{2}at^2[/tex]

 [tex]28=3u-\frac{1}{2}*9.8*3^2[/tex]

 [tex]u=24.03m/s[/tex]

Generally the velocity at  elevation and depression occurs  as ball arrives and passes through S=28

 [tex]v=\sqrt{24.03-2*9.8*28}[/tex]

 [tex]v=5.35m/s and -5.35m/s[/tex]

Generally the Newton's equation for time to reach initial velocity  is mathematically given by

 [tex]v=u+at[/tex]

 [tex]5.35=24.03-9.8t[/tex]

 [tex]t=\frac{28.03-5.35}{9.8}[/tex]

 [tex]t=1.9 sec[/tex]

An object with mass m = 0.56 kg is attached to a string of length r = 0.72 m and is rotating with an angular velocity ω = 1.155 rad/s. What is the centripetal force acting in the object?

Answers

Answer:

The centripetal force is 0.54 N.

Explanation:

mass, m = 0.56 kg

radius, r = 0.72 m

angular speed, w = 1.155 rad/s

The centripetal force is given by

[tex]F = m r w^2\\\\F =0.56\times 0.72\times 1.155\times 1.155\\\\F = 0.54 N[/tex]

An 8.50 kg point mass and a 14.5 kg point mass are held in place 50.0 cm apart. A particle of mass (m) is released from a point between the two masses 12.0 cm from the 8.50 kg mass along the line connecting the two fixed masses.Find the magnitude of the acceleration of the particle.

Answers

Answer:

[tex]a=2.8*10^{-9}m/s[/tex]

Explanation:

From the question we are told that:

First Mass [tex]m=8.50kg[/tex]

2nd Mass [tex]m=14.5kg[/tex]

Distance

[tex]d_1=50=>0.50m\\\\d_2=>12cm=>0.12m[/tex]

Generally the Newtons equation for Gravitational force is mathematically given by

[tex]F_n=\frac{Gm_nm}{(r_n)^2}[/tex]

Therefore

Initial force on m

[tex]F_1=\frac{Gm_1m}{(r_1)^2}[/tex]

Final force on m

[tex]F_2=\frac{Gm_2m}{(r_2)^2}\\\\F=\frac{Gm_1m}{(r_1)^2}-\frac{Gm_2m}{(r_2)^2}[/tex]

Acceleration of m

[tex]a=\frac{F}{m}\\\\a=\frac{Gm_1}{r_1^2}-\frac{Gm_2}{r_2^2}[/tex]

[tex]a=6,67*10^{-11}{\frac{8.5}{0.12}}-\frac{14.5}{0.50}[/tex]

[tex]a=2.8*10^{-9}m/s[/tex]

Human vision cuts off on the red side of the spectrum at about 675 nm. What is the energy of a photon (in J) of this wavelength?

Answers

Answer:

The energy of a photon is 2.94x10⁻¹⁹ J.

Explanation:

The energy of the photon is given by:

[tex] E = \frac{hc}{\lambda} [/tex]  

Where:

h: is Planck's constant = 6.62x10⁻³⁴ J.s

c: is the speed of light = 3.00x10⁸ m/s

λ: is the wavelength = 675 nm

Hence, the energy is:

[tex] E = \frac{hc}{\lambda} = \frac{6.62 \ccdot 10^{-34} J.s*3.00 \cdot 10^{8} m/s}{675 \cdot 10^{-9} m} = 2.94 \cdot 10^{-19} J [/tex]

Therefore, the energy of a photon is 2.94x10⁻¹⁹ J.

I hope it helps you!

can anyone answer this fast pls

Answers

i believe the answer would be 4.5. because it wouldnt be c or d. and 2 seems too small.

If the temperature of the conductor is increased, the electrons’ speeds decrease

Answers

Answer:

HOPE IT HELPS YOU!!!

Explanation:

Mark FadedGirl25 as brainliest

The wheels on a skateboard have a diameter of 2.93 inches. If a skateboarder is traveling downhill at 23 miles per​ hour, determine the angular velocity of the wheels in radians per second.

Answers

Answer:

The angular velocity of the wheels is 276.314 radians per second.

Explanation:

The wheels are rolling, which is a combination of rotation and translation, whose center of rotation is the point of contact between the wheel and the ground and the geometrical center of the skateboard experiments pure translation. Then, the angular velocity can be found by using the following kinematic expression:

[tex]\omega = \frac{v}{R}[/tex] (1)

Where:

[tex]\omega[/tex] - Angular velocity, in radians per second.

[tex]v[/tex] - Velocity of the wheel at its center, in inches per second.

[tex]R[/tex] - Radius of the wheel, in inches.

If we know that [tex]v = 404.8\,\frac{in}{s}[/tex] and [tex]R = 1.465\,in[/tex], then the angular velocity of the wheels are:

[tex]\omega = \frac{404.8\,\frac{in}{s} }{1.465\,in}[/tex]

[tex]\omega = 276.314\,\frac{rad}{s}[/tex]

The angular velocity of the wheels is 276.314 radians per second.

what is microeconomics ​

Answers

Answer:

Microeconomics is a part of economics and the study of decisions made by people and businesses regarding the allocation of resources, and prices at which they trade goods and services.

Microeconomics helps business planning i.e. helps the business community to plan their costs, production, etc. in anticipation of demand in order to maximize profits. Microeconomics is useful in explaining how market mechanism determines the price in a free market economy.

20. Using the picture, how many neutrons does lithium have?

Answers

Answer:

No. of Neutrons = 3

Explanation:

The atomic number of Lithium is given as 3 in the symbol while the mass number is given as 5.941 which is approximately equal to 6.

Mass Number = No. of Protons + No. of Neutrons = 6

Atomic Number = Number of Electrons = No. of Protons = 3

Therefore,

Mass Number - Atomic Number = (No. of Protons + No. of Neutrons) - No. of Protons

Mass Number - Atomic Number = No. of Neutrons

No. of Neutrons = 6 - 3

No. of Neutrons = 3

Answer:

3

Explanation:

Honestly, it is the only one in the picture and as an answer.

turn this scentence to repirted speach.

i ate icecream
She said that..........​

Answers

Answer:

dhfhffuththt9tr8tujtngigjtjrjrjrurur

Fvhjgxvbbdfhj if Dan kf xdhgxzsf

A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed (12 m/s), the total force on the driver has a magnitude of 146 N. What is the total vector force (in N) on the driver if the speed is 18 m/s instead?

Answers

Answer:

a1 =  v1^2 / R

a2 =  v2^2 / R

a2 = (v2 / v1)^2 = (3 / 2)^2 = 9/4

F2 = 9/4 * F1 = 9/4 * 146 = N     329 N      since F = m * a

(a) Suppose that a NASCAR race car is moving to the right with a constant velocity of +96 m/s. What is the average acceleration of the car? (b) Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the average acceleration of the car?

Answers

B. Tweleve seconds later the car is halfway

LC-circuit of the radio receiver consists of variable capacitor (Cmin= 1 pF, Cmax=10 pF) and inductor
with inductance 1 µH. Determine the wavelength range of this radio receiver.

Answers

Answer:

the radio can tune wavelengths between 1.88 and 5.97 m

Explanation:

The signal that can be received is the one that is in resonance as the impedance of the LC circuit.

         X = X_c - X_L

         X = 1 / wC - w L

at the point of resonance the two impedance are equal so their sum is zero

         X_c = X_L

         1 / wC = w L

         w² = 1 / CL

         w = [tex]\sqrt{\frac{1}{CL} }[/tex]

let's look for the extreme values

C = 1  10⁻¹² F

         w = [tex]\sqrt{\frac{1}{ 1 \ 10^{-12} \ 1 \ 10^{-6}} }[/tex]

         w = [tex]\sqrt{1 \ 10^{18}}[/tex]

         w = 10⁹ rad / s

C = 10 10⁻¹² F

         w = [tex]\sqrt{\frac{1}{10 \ 10^{-12} \ 1 \ 10^{-6}} }[/tex]Ra 1/10 10-12 1 10-6

         w = [tex]\sqrt{0.1 \ 10^{18}}[/tex]Ra 0.1 1018

         w = 0.316 10⁹ rad / s

Now the angular velocity and the frequency are related

           w = 2π f

           f = w / 2π

the light velocity  is

           c = λ f

           λ = c / f

we substitute

          λ = c 2π/w

               

we calculate the two values

 C = 1 pF

          λ₁ = 3 10⁸ 2π / 10⁹

          λ₁= 18.849 10⁻¹ m

          λ₁ = 1.88 m

C = 10 pF

           λ₂ = 3 10⁸ 2π / 0.316 10⁹

           λ₂ = 59.65 10⁻¹ m

           λ₂ = 5.97 m

so the radio can tune wavelengths between 1.88 and 5.97 m

voltage needed to raise current to 3.75a using 20,20,200 resistor set

Answers

Answer: The voltage needed is 35.7 V

Explanation:

Assuming that the resistors are arranged in parallel combination.

For the resistors arranged in parallel combination:

[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}[/tex]

We are given:

[tex]R_1=20\Omega\\R_2=20\Omega\\R_3=200\Omega[/tex]

Using above equation, we get:

[tex]\frac{1}{R}=\frac{1}{20}+\frac{1}{20}+\frac{1}{200}\\\\\frac{1}{R}=\frac{10+10+1}{200}\\\\R=\frac{200}{21}=9.52\Omega[/tex]

Calculating the voltage by using Ohm's law:

[tex]V=IR[/tex]         .....(1)

where,

V = voltage applied

I = Current = 3.75 A

R = Resistance = [tex]9.52\Omega[/tex]

Putting values in equation 1, we get:

[tex]V=3.75\times 9.52\\\\V=35.7V[/tex]

Hence, the voltage needed is 35.7 V

There are six different ways to arrange those resistors.

Each way leads to a different answer.

You didn't tell us how you want them connected.

The attached drawing shows them all.

Your car breaks down in the middle of nowhere. A tow truck weighing 4000 lbs. comes along and agrees to tow your car, which weighs 2000 lbs., to the nearest town. The driver of the truck attaches his cable to your car at an angle of 20 degrees to horizontal. He tells you that his cable has a strength of 500 lbs. He plans to take 10 secs to tow your car at a constant acceleration from rest in a straight line along a flat road until he reaches the maximum speed of 45 m.p.h. Can the driver carry out the plan

Answers

Answer:

F = 1010 Lb

the tension on the cable is greater than its resistance, which is why the plan is not viable

Explanation:

For this exercise we can use the kinematic relations to find the acceleration and with Newton's second law find the force to which the cable is subjected.

          v = v₀ + a t

how the car comes out of rest v₀ = 0

          a = v / t

let's reduce to the english system

          v = 45 mph (5280 ft / 1 mile) (1h / 3600) = 66 ft / s

let's calculate

          a = 66/10

          a = 6.6 ft / s²

now let's write Newton's second law

X axis

         Fₓ = ma

with trigonometry

         cos 20 = Fₓ / F

         Fₓ = F cos 20

we substitute

          F cos 20 = m a

          F = m a / cos20

          W = mg

          F = [tex]\frac{W}{g} \ \frac{a}{cos 20}[/tex]

let's calculate

          F = [tex]\frac{2000}{32} \ \frac{6.6 }{cos20}[/tex](2000/32) 6.6 / cos 20

          F = 1010 Lb

Under these conditions, the tension on the cable is greater than its resistance, which is why the plan is not viable.

Q2/Deceleration of a particle is based on relation a=-3 v² m/s² where v in m/s. If it moves along a straight line and has velocity 10 m/s and position s = 8m when t=0, determine its velocity and position when t= 3 s. Where the velocity become zero. Discuss briefly.​

Answers

Explanation:

Given: a = -3v^2

By definition, the acceleration is the time derivative of velocity v:

[tex]a = \frac{dv}{dt} = - 3 {v}^{2} [/tex]

Re-arranging the expression above, we get

[tex] \frac{dv}{ {v}^{2} } = - 3dt[/tex]

Integrating this expression, we get

[tex] \int \frac{dv}{ {v}^{2} } = \int {v}^{ - 2}dv = - 3\int dt[/tex]

[tex] - \frac{1}{v} = - 3t + k[/tex]

Since v = 10 when t = 0, that gives us k = -1/10. The expression for v can then be written as

[tex] - \frac{1}{v} = - 3t - \frac{1}{10} = - ( \frac{30 + 1}{10} )[/tex]

or

[tex]v = \frac{10}{30t +1 } [/tex]

We also know that

[tex]v = \frac{ds}{dt} [/tex]

or

[tex]ds = vdt = \frac{10 \: dt}{30t + 1} [/tex]

We can integrate this to get s:

[tex]s = \int v \: dt = \int ( \frac{10}{30t + 1}) \: dt = 10 \int \frac{dt}{30t + 1} [/tex]

Let u = 30t +1

du = 30dt

so

[tex] \int \frac{dt}{30t + 1} = \frac{1}{30} \int \frac{du}{u} = \frac{1}{30}\ln |u| + k[/tex]

[tex]= \frac{1}{30}\ln |30t + 1| + k[/tex]

So we can now write s as

[tex]s = \frac{1}{3}\ln |30t + 1| + k[/tex]

We know that when t = 0, s = 8 m, therefore k = 8 m.

[tex]s = \frac{1}{3}\ln |30t + 1| + 8[/tex]

Next, we need to find the position and velocity at t = 3 s. At t = 3 s,

[tex]v = \frac{10}{30(3) +1 } = \frac{10}{91}\frac{m}{s} = 0.11 \: \frac{m}{s} [/tex]

[tex]s = \frac{1}{3}\ln |30(3) + 1| + 8 = 9.5 \: m[/tex]

Note: velocity approaches zero as t --> [tex]\infty [/tex]

A stone was dropped off a cliff and hit the ground with a speed of 136 ft/s. What is the height of the cliff

Answers

Answer:

Explanation:

Use the equation

[tex]v^2=v_0^2+2a[/tex]Δx

In this dimension (the y dimension...the only one we have to care about for this problem), here's what we know:

a = -32 ft/s/s

v₀ = 0 m/s (since someone was holding the stone still before it was dropped)

v = 136 ft/s

Δx = ??

Filling in:

[tex]136^2=0^2+2(-32)[/tex]Δx so

Δx = [tex]\frac{136^2}{2(-32)}[/tex] so

Δx = -289 feet (negative because the stone dropped that many feet below the point from which it was dropped, but you would answer a height question with the positive of this number. If you were asked how far the stone dropped, it would be negative; if you're asked how tall the cliff is, that would be positive)

which of the following is a correct statement. a. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are constant. b. In dc steady state conditions, the voltages across the capacitors are zero and the currents through the capacitance are constant. The current through the inductors are constant and the voltage across the inductances are zero. c. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are zero and the voltage across the inductances are constant. d. WIn dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.

Answers

Answer:

d. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.

Explanation:

The current through a capacitor is given by i = CdV/dt where C = capacitance of capacitor and V = voltage across capacitor. At steady state dV/dt = 0 and V = constant. So, i = CdV/dt = C × 0 = 0.

So, in dc steady state, the voltage across a capacitor is constant and the current zero.

The voltage across an inductor is given by V = Ldi/dt where L = inductance of inductor and i = current through inductor. At steady state di/dt = 0 and V = constant. So, V = Ldi/dt = L × 0 = 0.

So, in dc steady state, the voltage across an inductor is zero and the current constant.

So, In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.

The answer is d.

A 0.0780 kg lemming runs off a
5.36 m high cliff at 4.84 m/s. What
is its kinetic energy (KE) when it
is 2.00 m above the ground?

Answers

Answer:

0.913

Explanation:

k.e=1/2mv square

k.e=1/2×0.078g×23.4256m/s square

k.e=0.913J

The kinetic energy when the lemming is 2.00 m above the ground is approximately 2.56 J (Joules).

To calculate the kinetic energy (KE) of the lemming when it is 2.00 m above the ground, we need to consider the change in its potential energy (PE) as it falls.

The potential energy at a height h is given by:

PE = m g h

Where:

m is the mass of the lemming (0.0780 kg)

g is the acceleration due to gravity (9.8 m/s²)

h is the height above the ground

Given:

Height of the cliff (h) = 5.36 m

Velocity of the lemming (v) = 4.84 m/s

Height above the ground (h') = 2.00 m

The lemming will lose potential energy as it falls from the cliff, which is converted into kinetic energy. Therefore, the kinetic energy when it is 2.00 m above the ground is equal to the difference between its total initial kinetic energy and the potential energy at that height.

Initial potential energy at the top of the cliff:

PE_initial = m g h

Potential energy when it is 2.00 m above the ground:

PE_final = m * g * h'

The change in potential energy is given by:

ΔPE = PE_final - PE_initial

The kinetic energy (KE) when it is 2.00 m above the ground:

KE = ΔPE = -ΔPE (due to energy conservation)

Let's calculate the potential energy at the top of the cliff and when it is 2.00 m above the ground:

PE_initial = m ×g × h

= 0.0780 kg × 9.8 m/s² × 5.36 m

PE_initial ≈ 4.09 J

PE_final = m ×g × h'

= 0.0780 kg ×9.8 m/s² ×2.00 m

PE_final ≈ 1.53 J

The change in potential energy (ΔPE) is:

ΔPE = PE_final - PE_initial = 1.53 J - 4.09 J

ΔPE ≈ -2.56 J

Since the change in potential energy is equal to the kinetic energy, the kinetic energy when the lemming is 2.00 m above the ground is approximately 2.56 J (Joules).

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