. Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device produces 10.0 kW of power on a day when the breakers are 1.20 m high, how much will it produce when they are 0.600 m high?

Answer:

greater than 0.10

Explanation:

The null hypothesis is:

[tex]H_{0} = 10.2[/tex]

The alternate hypotesis is:

[tex]H_{1} > 10.2[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the statistic, [tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

We have that:

[tex]t = 0.45[/tex]

We are testing if X is greater than 0.45, so our pvalue is 1 subtracted by the pvalue of z = t = 0.45.

z = 0.45 has a pvalue of 0.6736

1 - 0.6735 = 0.3264

So our pvalue is 0.3264, which is greater than 0.10.

So the correct answer is:

greater than 0.10

Here the test sta-tis-tics should be greater than 0.10.

Since In 1990s, the average amount of time spent playing computer games was 10.2 hours per week.

Here, t = 0.45

So in the case when X is greater than 0.45, so our pvalue is 1 subtracted by the p-value of z = t = 0.45.

z = 0.45 has a p-value of 0.6736

1 - 0.6735 = 0.3264

Now

our p-value is 0.3264, which is greater than 0.10.

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Answer:

Length,  Area, Conductivity, Temperature

Explanation:

The factors affection the resistance of a conductor are

(1) Length of the conductor (L): As the length (L) of the conductor increases, the Resistance(R) of the conductor also increase.

R ∝ L

(2) Cross sectional Area of the conductor(A): As the cross sectional area of the conductor(A) increases, the Resistance (R) of the of the conductor decreases.

R ∝1/A

(3)  conductivity of the conductor(G): As the conductivity of the (G) of the conductor increases, the Resistance(R) of the conductor decreases.

R ∝ 1/G

(4) Temperature(T): As temperature(T) increases, the Resistance(R) of a conductor decreases.

T ∝ R

Answer:

Explanation:

There are four factors affecting resistance which are

Temperature,

Length of wire,

Area of the cross-section of wire and

nature of the material.

Answer:

[tex]-\frac{F_2}{m_1}[/tex]

Explanation:

First of all, we notice that the collision is elastic: this means that there are no external forces acting on the system, as the total momentum and the total kinetic energy of the system are conserved.

The force acting on the cart 2 is

[tex]F_2[/tex]

According to Newton's third law of motion:

"When an object 1 exerts a force on another object 2, then object 2 exerts an equal and opposite force on object 1"

Therefore, if we call [tex]F_1[/tex] the force exerted on cart 1 during the collision, we can write

[tex]F_1=-F_2[/tex]

According to Newton's second law of motion, the net force acting on an object is equal to the product between its mass (m) and its acceleration (a):

[tex]F=ma[/tex]

So for cart 1 we have:

[tex]F_1=m_1 a_1[/tex]

And som the acceleration of cart 1 is

[tex]a_1=\frac{F_1}{m_1}=-\frac{F_2}{m_1}[/tex]

Where the negative sign means that the direction of the acceleration of cart 1 is opposite to the direction of the force F2.

Answer:

The magnetic flux through the two cubes is zero in both cases

Explanation:

To answer this question, we have to think about the nature of magnetic fields.

In fact, we know that magnetic sources always exist only as magnetic dipoles: this means that a magnet always has a north pole (from which the magnetic field lines go away) and a south pole (into which the magnetic field lines return). There exist no magnetic monopoles: even when we cut a magnet in a half, we end up having two magnets, each of them having its own north pole and south pole.

A direct consequence of this fact is that if we take a closed surface, such as a cube surrounding the magnet, the magnetic flux through the cube is always zero. This is because all the field lines going out the surface of the cube always return inside the cube on another point. Since the magnetic flux basically represents the number of field lines passing through the surface of the cube, this means that the net positive magnetic flux (lines going out of the cube) is equal to the net negative magnetic flux (lines going into the cube).

As a result, the magnetic flux is zero for both the smaller cube and the larger cube.

You really can't tell.

Power = I^2 × R = V^2 / R ( unit in Watt)

For P = I^2 × R

Where we have P directly proportional to R, increase in Power leads to increase in R

So if we have 100 will have higher resistance

For P = V^2/R

Power is inversely proportional to resistance.

So increase in Power leads to decrease in resistance.

60 watt will have a higher resistance.

Answer:

[tex]5.868 \times 10^7 Pa[/tex]

Explanation:

If half the gas is drawn then pressure would have dropped by half

[tex]P_1 = 10^8 /2 = 5\times10^7 Pa[/tex]

Assuming ideal gas, if temperature rises from 15c (T1 = 15 + 273 = 288 K) to 65 c (T2 = 65 + 273 = 338 K), then we have the following equation for ideal gas

[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]

[tex]P_2 = T_2\frac{P_1}{T_1} = 338\frac{5\times10^7}{288} = 5.868 \times 10^7 Pa[/tex]

Answer:

Relative dating involves the dating of geological events and

formations that occured/existed throughout the whole geological

history, and this eventually gives the relative age of the earth.

While, Absolute dating involves the use of isotopes and radioactive

elements (radioactivity) and also the study and relation of

meteorites and moon rocks, which eventually gives the   actual/absolute age of the earth. The meteorites and moon rocks are

believed to have formed virtually at the same time with earth and

are therefore, considered to be of the same age as earth.

Explanation:

Answer:

Absolute dating and relative dating are both methods used to determine the age of a fossil. Absolute dating gives the actual age of a fossil in years based on the amount of radioactive and stable elements in the fossil. Relative dating gives an estimate of the age of a fossil based on the location of the fossil in relation to other fossils.  

Explanation:

sample response

The type of movement used as an input includes gliding, angular, rotational, or special movement. These movements refer to instances like bone surfaces moving past each other, changes in the angle between joint bones, rotation of a bone around its own axis, and specific non-classifiable movements.

The type of movement used as an input varies depending on the situation and mechanism in question. In the broader sense, common types of movement used as inputs include: gliding, angular, rotational, or special movement.

Gliding movements occur as flat bone surfaces move past each other, such as the joints of the carpal and tarsal bones. Angular movements change the angle between bones of a joint, observed in actions like flexion and extension. Rotational movements result in the rotation of a bone around its own axis, while special movements that don't fit into the previous categories involve specific movements, like inversion, eversion, protraction, retraction, elevation, depression, dorsiflexion, plantar flexion, supination, pronation, or opposition.

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Answer:

a) [tex]k = 200.016\,\frac{N}{m}[/tex], b) [tex]m = 1.389\,kg[/tex], c) [tex]f = 0.524\,hz[/tex]

Explanation:

a) The maximum speed of the oscillating block-spring system is:

[tex]v_{max} = \omega \cdot A[/tex]

The angular frequency is:

[tex]\omega = \frac{v_{max}}{A}[/tex]

[tex]\omega = \frac{1.2\,\frac{m}{s} }{0.1\,m}[/tex]

[tex]\omega = 12\,\frac{rad}{s}[/tex]

The mass of the system is:

[tex]E = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex]

[tex]m = \frac{2\cdot E}{v_{max}^{2}}[/tex]

[tex]m = \frac{2\cdot (1\,J)}{(1.2\,\frac{m}{s} )^{2}}[/tex]

[tex]m = 1.389\,kg[/tex]

The spring constant is:

[tex]\omega = \sqrt{\frac{k}{m} }[/tex]

[tex]k = \omega^{2}\cdot m[/tex]

[tex]k = (12\,\frac{rad}{s} )^{2}\cdot (1.389\,kg)[/tex]

[tex]k = 200.016\,\frac{N}{m}[/tex]

b) The mass is:

[tex]m = 1.389\,kg[/tex]

c) The frequency of oscillation is:

[tex]\omega = 2\pi\cdot f[/tex]

[tex]f = \frac{2\pi}{\omega}[/tex]

[tex]f = \frac{2\pi}{12\,\frac{rad}{s} }[/tex]

[tex]f = 0.524\,hz[/tex]

Answer:

a) F = 20 N

b) m = 1.39 kg

c) f = 1.909 Hz

Explanation:

Given

E = 1 J

A = 0.1 m

vmax = 1.2 m/s

a) F = ?

b) m = ?

c) f = ?

Solution

a) We apply the equation

E = 0.5*k*A²

then

k = 2*E/A²

k = 2*1 J/(0.1 m)²

k = 200 N/m

then we use the equation

F = kA

F = (200 N/m)(0.1 m)

F = 20 N

b) We use the formula

E = K + U

if U = 0 J

then

E = K = 0.5*m*v²

⇒  m = 2*K/v²

m = 2*1 J/(1.2 m/s)²

m = 1.39 kg

c) we apply the equation

f = (1/2π)√(k/m)

then

f = (1/2π)√(200 N/m/1.39 kg)

f = 1.909 Hz

Answer:the fields are at right angles to each other and to the direction of the wave.

Explanation: gradpoint

In relation to the electromagnetic spectrum,wavelength is defined as a distance between peak of waves. It goes on decreasing from moving left to right in the electromagnetic spectrum as the energy increases.

The electromagnetic spectrum consists of  radiation  which consists of waves made up of the  electromagnetic field which are capable of propogating through space and carry the radiant electromagnetic energy.

The radiation are composed of electromagnetic waves which are synchronized oscillations of electric and magnetic fields . They are created due to change which is periodic in electric as well as magnetic fields.

In vacuum ,all the electromagnetic waves travel at the same speed that is with the speed of air.

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Answer:

Explanation:

Lightning is seen before the thunder is heard because , velocity of light exceeds velocity of sound. We also know that velocity , wavelength and frequency are related as follows

velocity = frequency x wavelength

velocity of light > velocity of sound

frequency of light x wavelength of light > frequency of sound x wavelength of sound

But given wavelength of light = wavelength of sound

Putting this relation in the equation above

frequency of light x wavelength of light > frequency of sound x wavelength of light

cancelling out equal terms on both sides

frequency of light  > frequency of sound

frequency of light will be greater than frequency of sound.

Answer:

the frequency of thunder is more than the frequency of lightning

Explanation:

Light waves (lightning) are faster than sound waves (thunder). If their wavelengths are the same, then the frequency of light waves must be larger

Refrigerators and air conditioners use heat transfer, requiring a work input, to move thermal energy from cooler to warmer spaces. They absorb thermal energy from the cooler area, transfer it to a hotter reservoir while discharging heat back into the environment. These are essentially heat engines run backward, not in strict reverse.

Contrary to what may seem natural, appliances like refrigerators and air conditioners utilize a concept known as heat transfer to move thermal energy from a cooler space to a warmer one. This process requires a work input, typically provided by a motor or cooling substance.

The process occurs in stages. Firstly, the appliance absorbs thermal energy (denoted as Qc) from the cooler area. Secondly, this energy is transferred to a hotter reservoir, simultaneously discharging thermal energy (Qh) back into the warmer environment. The work input (W) is crucial here as it aids in moving the energy from the cool to the warm region, thereby keeping the cooler region at a lower temperature.

Finally, it's important to remember that these systems don't exactly run in reverse. Instead, they are essentially heat engines run backward, implying that while they perform opposite functions, they don't strictly follow a reversed process of a heat engine.

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1) 0.00257 A

2) [tex]1.6\cdot 10^{17}[/tex] electrons

3) 0.00512 A

Explanation:

1)

A current is defined as the flow of charge through a conductor.

The intensity of current is calculated as:

[tex]I=\frac{q}{t}[/tex] (1)

where

q is the amount of charge passing through a certain point in the conductor

t is the time interval during which this charge passes

In the wire in this problem we have:

[tex]q=9.0 mC=0.009 C[/tex] is the charge

[tex]t=3.5 s[/tex] is the time elapsed

Therefore, the current in the wire is:

[tex]I=\frac{0.009}{3.5}=0.00257 A[/tex]

2)

To find the total charge passing through a given point of the wire in a certain time, we re-arrange eq. (1):

[tex]q=It[/tex]

where

I is the current

t is the time interval we are considering

In this problem we have:

I = 0.00257 A is the current in the wire

t = 10.0 s is the time we are considering

Therefore, the charge is:

[tex]q=(0.00257)(10.0)=0.0257 C[/tex]

We know that this charge q consists of N electrons, so we can write

[tex]q=Ne[/tex]

where

[tex]e=1.6\cdot 10^{-19}C[/tex] is the charge of one electron

Solving for N, we find:

[tex]N=\frac{q}{e}=\frac{0.0257}{1.6\cdot 10^{-19}}=1.6\cdot 10^{17}[/tex]

3)

In this problem, we are told that the number of charges that pass through the cross-sectional area during the given time interval doubles, so we have:

[tex]N'=2N=2(1.6\cdot 10^{17})=3.2\cdot 10^{17}[/tex]

Therefore, the total charge through the point in the wire in a time of

t = 10.0 s

will be

[tex]q'=N'e=(3.2\cdot 10^{17})(1.6\cdot 10^{-19})=0.0512 C[/tex]

And so, the current in this case will be

[tex]I'=\frac{q'}{t}=\frac{0.0512}{10.0}=0.00512 A[/tex]

And we see that this current is twice the current we had in part 1), because the current is proportional to the number of charge carriers.

The charges are  [tex]0.00257\ A[/tex],  [tex]1.6 \times 10^{17}[/tex] electrons, and [tex]0.00512 \ A[/tex], and their further calculation can be defined as follows:

For part 1:

A movement of energy via a conductor is known as just a current.

This current's strength is computed as:

[tex]I=\frac{q}{t}.....(1)[/tex]

wherein q is the quantity of charge travelling through a specific location in the conductor, and t denotes a time interval during which this charge flows.

In the this problem, we have the following wire:

[tex]\to q=9.0 \ m C=0.009\ C[/tex] charges  

Time elapsed [tex]t=3.5 \ s[/tex]

current wire:

[tex]\to I=\frac{0.009}{3.5}= 0.00257 \ A[/tex]

For part 2:

You re-arrange eq. (1) to obtain that total charge passing through a particular location of the wire inside a given time.

[tex]\to q=It\\\\[/tex]

where

current =I

interval time =t

[tex]I = 0.00257\ A[/tex]  current in the wire

[tex]t = 10.0\ s[/tex]

Calculating the charge:

[tex]\to q=(0.00257) (10.0) =0.02575\ C[/tex]

We assume there are N electrons in this test charge, thus we can write

[tex]q=Ne\\\\[/tex]

where

Calculating the charge in one electron

[tex]e=1.6 \times 10^{-19}\ C[/tex]

Solving for N:

[tex]\to N=\frac{q}{e}=\frac{0.0257}{1.6\times 10^{-19}}=1.6 \times 10^{17}\\\\[/tex]

For point 3:

A number of charges which it pass through the cross-sectional area during the given time interval doubles in this issue, so we have:

[tex]\to N'=2N=2(1.6 \times 10^{17})=3.2\times 10^{17}\\\\[/tex]

As a result, the complete charge passed through the wire point in a period of

[tex]t = 10.0\ s\\\\[/tex]

[tex]\to q'=N'e=(3.2\times 10^{17})(1.6\times 10^{-19})=0.0512\ C\\\\[/tex]

So, in this scenario, the current will be

[tex]\to I'=\frac{q'}{t}=\frac{0.0512}{10.0}=0.00512\ A\\\\[/tex]

Because the current is proportional to the number of charge carriers, we can see that this current is twice as large as the current we had in part 1.

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Answer:

Steam-methane reforming

Electrolysis of water

Explanation:

Steam methane reforming involves reaction of methane with water in the presence of a catalyst such as nickel to form Carbon oxides and Hydrogen.

CH4 + H2O ⇌ CO + 3 H

Electrolysis of water involves splitting of water through application of electric current to give Hydrogen and Oxygen gas.

2 H2O(l) → 2 H2(g) + O2(g)

Hydrogen gas for fuel cells is commonly produced through steam reforming and electrolysis. In steam reforming, steam is passed over coke to produce hydrogen and carbon monoxide. In electrolysis, water is split into hydrogen and oxygen gases with a power supply.

The two most common ways to produce hydrogen gas used in fuel cells are through steam reforming and electrolysis. Steam reforming involves passing steam over coke at high temperatures, which produces a mixture of carbon monoxide and hydrogen gas, also known as water gas.

In the electrolysis process, water is split into hydrogen and oxygen gases by the addition of energy using a battery or power supply. For fuel cells, hydrogen obtained from these processes is continuously fed into the cell with an oxidant and undergoes redox chemistry that generates electrical energy and water as the waste product. The fuel cell reactions are catalyzed on graphite electrodes embedded with platinum-based catalysts.

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Answer:

Potential energy is converted into kinetic energy by a force. For example, when you pick up a rock, you work against gravity to give it some potential energy. And then when you drop it, the gravitational force causes the rock to accelerate towards the ground

Explanation:

Potential energy is transformed into kinetic energy through various natural processes. An example is a rollercoaster which at the peak has high potential energy due to its height, but as it descends and increases speed, the potential energy is transformed into kinetic energy. This phenomenon is guided by the Law of Conservation of Energy.

In physics, potential energy is stored energy that an object has due to its position or state. Kinetic energy on the other hand, is the energy that an object possesses due to its motion. The transformation between these two forms of energy occurs continuously in the natural world.

For instance, think of a rollercoaster at the peak of a track. It has a high potential energy because of its height. As the rollercoaster starts to descend, the potential energy is transformed into kinetic energy as the rollercoaster increases speed (due to gravity). When it gets to the lowest point, all of its potential energy has been converted into kinetic energy. This cycle continues for the duration of the ride, with the rollercoaster's energy constantly being transformed between potential and kinetic.

This transformation between potential and kinetic energy is referred to as the Law of Conservation of Energy, which states that energy cannot be created or destroyed, it can only be transformed from one form to another.

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Answer:

7.33 rounded

Explanation:

Speed = distance divided time

S = d/t

Suppose a Rollerblade racer finished a 132 meter race in 18 seconds. What is the average speed of the Rollerblade racer?

S = 132 divided 18

Speed = 7.33 rounded

Answer: 7.3 meters a second

Explanation: 132/18=7.3

Answer:

Parked truck

Fast feather

fast baseball

slow car

fast car

Answer:

-5.8 m/s

Explanation:

Given:-

- The mass of Big Bubba, mb = 125 kg

- The mass of Lil' Pete, mp = 80 kg

- The initial velocity of Big Bubba, vb = 7 m/s

- The initial velocity of Lil Pete , vp = -10 m/s

- The velocity after impact of Lil' Pete, vp' = + 10 m/s

- The velocity after impact of Big Bubba = vb'

Find:-

what is  Big Bubba's velocity after the collision?

Solution:-

- We will consider the two football players as particles of mass mb and mp with their respective velocities vb and vp heading towards each other.

- The masses collide and both reverse in direction with velocities vb' and vp'.

- The system of the two masses have no external forces acting on it; hence, the system is isolated from any fictitious forces.

- For above conditions we can apply the principle of conservation of linear momentum. The linear momentum of two football players before ( Pi ) and after the impact ( Pf ) remain constant. The conservation is:

                             Pi = Pf

           mb*vb + mp*vp = mb*vb' + mp*vp'

           mb*vb + mp*( vp - vp' ) = mb*vb'

- Develop an expression for Big Bubba's velocity after impact vb':

           vb' = vb + mp/mb*( vp - vp' )

- Plug in the values and evaluate:

         vb' = 7 + 80/125*( -10 - 10 )

         vb' = 7 - 80*20 / 125

          vb' = -5.8 m/s  

Answer: The velocity of Big Bubba after impact is vb' = -5.8 m/s

Answer:

The heater use 583 kWh of electrical energy per month.

Explanation:

Given that,

Power of the water heater, P = 550 watts

It is operated for 106 hours

The electrical energy used by the heater per unit time is called its power. So,

[tex]P=\dfrac{E}{t}\\\\E=P\times t\\\\E=5500\ W\times 106\ h\\\\E=583000\ Wh\\\\E=583\ kWh[/tex]

So, the heater use 583 kWh of electrical energy per month.

Answer:D

Explanation:

Answer:

d.

Explanation:

Using Hooke's Law, we determined the spring constant to be approximately 1230 N/m. For a 3.3 kg mass, the extension is 2.63 cm. Therefore, the total length of the spring is 9.63 cm.

To find the length of the spring when a 3.3 kg mass is suspended from it, we need to determine the spring’s force constant (k). Using Hooke's Law, F = kx, where F is the force due to the mass, k is the spring constant, and x is the extension. First, convert the masses to forces (F = mg) using g = 9.8 m/s².

Now, we use this constant to find the extension for the 3.3 kg mass:

Add the extension to the original spring length:

New length of the spring: 7 cm + 2.63 cm = 9.63 cm.

Answer:10 hz

Explanation

A wave has a speed of 30 m/s and a wavelength of 3 meters then its frequency is 10 Hz.

Wave is is a disturbance in a medium that carries energy as well as momentum . wave is characterized by amplitude, wavelength and phase. Amplitude is the greatest distance that the particles are vibrating. especially a sound or radio wave, moves up and down. Amplitude is a measure of loudness of a sound wave. More amplitude means more loud is the sound wave.

Wavelength is the distance between two points on the wave which are in same phase. Phase is the position of a wave at a point at time t on a waveform.

There are two types of the wave longitudinal wave and transverse wave.

Longitudinal wave : in which, vibration of the medium (particle) is parallel to propagation of the wave. Sound wave is a longitudinal wave.

Transverse wave : in which, vibration of the medium (particle) is perpendicular to propagation of the wave. Light wave is a transverse wave.

Frequency of the wave is given by,

f = c/λ

f = 30/3 = 10 Hz

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Answer:

[tex]1.11\times10^{-4} C[/tex]

Explanation:

Coulomb's force:

[tex]F=\frac{kqq'}{d^2}[/tex]

where, q and q' are two charges, d is the distance between them and k is the Coulomb constant.

The net force on charge q at origin is 17 N.

[tex]17 = 9\times 10^9 \times 8.5\times10^{-6}[\frac{-28\times 10^{-6}}{0.21^2}+\frac{q_2}{0.36^2}]\\17 = 76.5 \times 10^3[-6.35 \times 10^{-4}+7.72q_2]\\q_2 = 1.11\times10^{-4} C[/tex]

Answer:

5.35 x 10^-5 C

Explanation:

q1 = - 28 micro Coulomb =- 28 x 10^-6 C

q2 = ?

q3 = 8.5 micro Coulomb = 8.5 x 10^-6 C

y1 = 0.21 m

y2 = 0.36 m

q3 is at origin.

Let F1 is the force between q1 and q3 and F2 is the force between q2 and q3.

By use of Coulomb's law, the force between the two charges is given by

[tex]F = \frac{Kqq'}{r^{2}}[/tex]

Now, [tex]F_{1} = \frac{Kq_{1}q_{3}}{0.2^{2}}[/tex]

[tex]F_{1} = \frac{9\times 10^{9}\times 28\times 10^{-6}\times 8.5\times 10^{-6}}{0.21^{2}}[/tex]

F1 = 48.6 N    .... (1)

Now, [tex]F_{2} = \frac{Kq_{2}\times q_{3}}{0.36^{2}}[/tex]

[tex]F_{2} = \frac{9\times 10^{9}\times q_{2} \times 8.5\times 10^{-6}}{0.36^{2}}[/tex]

F2 = 590277.78 q2   .... (2)

Now, F1 - F2 = 17

48.6 - 590277.78 q2 = 17     from (1) and (2)

q2 = 5.35 x 10^-5 C

Thus, the charge on q2 is 5.35 x 10^-5 C.  

Answer:

Speed of the car around the circular path will be 12 m/sec

Explanation:

We have given mass of the car m = 1500 kg

Radius of the curve r = 45 m

Centripetal acceleration of the car [tex]a=3.2m/sec^2[/tex]

We have to find the speed of the car

We know that centripetal acceleration is given by [tex]a=\frac{v^2}{r}[/tex], here v is car speed along the circular path and r is radius of the curve

So [tex]3.2=\frac{v^2}{45}[/tex]

[tex]v^2=144[/tex]

v = 12 m/sec

So speed of the car around the circular path will be 12 m/sec

The car's speed as it travels around the curve is 12m/sec.

Given that,

Based on the above information, the calculation is as follows:

[tex]3.2 = v^2 \div 45\\\\v^2 = 144[/tex]

v = 12

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Answer:

Red Dwarf

Explanation:

Answer:

[tex]\Delta h = 5.212\,m[/tex]

Explanation:

The inelastic collision is modelled by using the Principle of Momentum Conservation:

[tex](3.8\,kg)\cdot (19\,\frac{m}{s} ) + (1.6\,kg)\cdot (-11\,\frac{m}{s} ) = (3.8\,kg + 1.6\,kg)\cdot v[/tex]

The final velocity is:

[tex]v = 10.111\,\frac{m}{s}[/tex]

The maximum height of the composite system is:

[tex](0\,\frac{m}{s})^{2} = (10.111\,\frac{m}{s} )^{2} - 2\cdot (9.807\,\frac{m}{s^{2}} )\cdot \Delta h[/tex]

[tex]\Delta h = 5.212\,m[/tex]

Answer:

5.21m

Explanation:

We are given that;

mass of first ball; m1 = 3.8kg

Speed of first ball; v1 = 19 m/s upwards

Mass of second ball; v2 = 1.6 kg

Speed of second ball; v2 = 11 m/s downwards

From conservation of linear momentum,

m1v1 + m2v2 = m_t•v_t

Where,

m1v1 is momentum of first ball

m2v2 is momentum of second ball

m_t•v_t is the combined momentum of the 2 balls.

Let's make v_t the subject

v_t = [m1v1 + m2v2]/m_t

m_t is the combined mass of both balls.

Since first and second ball are moving in opposite directions, thus;

v_t = [m1v1 - m2v2]/m_t

Thus, m_t = 3.8 + 1.6 = 5.4kg

Thus, plugging in the relevant values, we have;

v_t = [(3.8 x 19) - (1.6 x 11)]/5.4

v_t = [(3.8 x 19) - (1.6 x 11)]/5.4

v_t = (72.2 - 17.6)/5.4

v_t = 54.6/5.4 = 10.11 m/s

Now, from equation of motion,

v² = u² + 2gh

Where u is initial velocity which is now v_t while final velocity v is zero.

Now, since gravity is acting against motion, g = - 9.8m/s²

Thus,

v² = u² + 2gh gives;

0² = 10.11² - (2 x 9.8 x h)

19.6h = 102.212

h = 102.212/19.6

h = 5.21 m

Answer:

[tex]\omega = 0.016\,\frac{rad}{s}[/tex]

Explanation:

The rotation rate of the man is:

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

[tex]\omega = \frac{0.80\,\frac{m}{s} }{5\,m}[/tex]

[tex]\omega = 0.16\,\frac{rad}{s}[/tex]

The resultant rotation rate of the system is computed from the Principle of Angular Momentum Conservation:

[tex](90\,kg)\cdot (5\,m)^{2}\cdot (0.16\,\frac{rad}{s} ) = [(90\,kg)\cdot (5\,m)^{2}+20000\,kg\cdot m^{2}]\cdot \omega[/tex]

The final angular speed is:

[tex]\omega = 0.016\,\frac{rad}{s}[/tex]

Using the principle of conservation of angular momentum, the person's movement imparts an angular velocity of 0.018 rad/s to the disk.

To solve this problem, we'll need to use the principle of conservation of angular momentum, which states that the total angular momentum before an event must equal the total angular momentum after the event if no external torques act on the system.

Given Data:

First, calculate the person's moment of inertia relative to the center of the disk:

Initial angular momentum of the person (since they are initially stationary) is 0.

When the person starts moving, they contribute angular momentum relative to the axis:

Since the merry-go-round was initially stationary, its initial angular momentum L(disk-initial) is 0.

By conservation of angular momentum, the total angular momentum before must equal the total angular momentum after:

Solving for the angular velocity ω of the disk:

Hence, the disk will rotate with an angular velocity of 0.018 rad/s in the direction opposite to the person’s motion due to the conservation of angular momentum.

Answer:yes it isss

Explanation: