A particle with a mass of 9.00 ✕ 10-20 kg is vibrating with simple harmonic motion with a period of 3.00 ✕ 10-5 s and a maximum speed of 7.00 ✕ 103 m/s. (a) Calculate the angular frequency of the particle. rad/s (b) Calculate the maximum displacement of the particle.

Answer:

5.5 N

Explanation:

Weigh of floating ball=5.5 N

Acceleration due to gravity=9.8 [tex]m/s^2[/tex]

We have to find the size of the buoyant force that acts on it.

We know that

Buoyant force is that force which act in upward direction and exert by fluid and opposes the weight of an immersed object.

Therefore,

Buoyant force=Weight of ball

Buoyant force=5.5 N

Hence, the size of buoyant force acts on the ball=5.5 N

Given the ball's weight of 5.5 N, the buoyant force is also 5.5 N.

To determine the buoyant force acting on a floating ball, we can use the principles of buoyancy and the given information about the ball's weight. The ball's weight in air is 5.5 N, and we know the acceleration due to gravity (g) is 9.8 m/s².

For a floating object, the buoyant force (Fb) is equal to the weight of the object when it is floating. Therefore, since the ball is floating, the buoyant force must equal the weight of the ball:

Buoyant force Fb = Weight of the ball

Given that the weight of the ball is 5.5 N, the buoyant force acting on the ball is:

Fb = 5.5 N

This force is what keeps the ball afloat in the fluid.

Answer: A. Vb1 = -6m/s , Vb2 = 9m/s.

B. Vb1 = 4.5m/s , Vb2 = 4.5m/s

Explanation: A. In a perfectly elastic collision the objects involved moved with a different velocity after collision. Also kenitic energy is conserved. In other to get the different velocity of ball 1 (Vb1) and ball 2 (Vb2) after collision, we apply the following formula

Vb1 = {{m1 - m2}*V1}/{m1 +m2}

Vb2 = {{2m1}*V1}/{m1 + m2}

Where V1 = velocity of ball 1 before collision=15m/s

m1 = mass of ball 1

m2 = mass of ball 2.

Substituting in the above equation:

Vb1 = {{0.15kg - 0.35kg}*15}/{0.15 + 0.35}

= {{-0.2}*15}/0.5

= -3/0.5

= -6m/s

Also,

Vb2 = {{2*0.15kg}*15m/s}/{0.15kg + 0.35kg}

={0.3kg*15m/s}/0.5kg

=4.5/0.5

=9m/s

B. In a perfectly inelastic collision the object involved move with a common velocity after collision.

We have that ,

m1*V1 + m2*v2 = {m1 + m2} V¹

Where V¹ is the final velocity of both balls after a perfectly inelastic collision.

NOTE: v2 here is 0m/s since ball 2 was at rest before collision.

So we have,

0.15kg*15m/s + 0.35kg*0m/s = {0.15kg + 0.35kg}*V¹

2.25 kgm/s = 0.5kg* V¹

Making V¹ subject of formula we have,

V¹ = 2.25kgm per sec/0.5kg

=4.5m/s. vb1 = Vb2 = V¹

NOTE also that the mass of the balls from the question were given in gram hence we converted to kilogram the standard unit for mass by dividing by 1000.

Answer:

For both ball 1 and ball 2, the change in velocity is less in an inelastic collision.

Explanation:

a short simple answer

Answer:

d. Critical transportation; situation assessment; and mass care services

Explanation:

The correct answer is option d which is Critical transportation: Situation assessment and mass care services are core capabilities for response.  

As we know that critical transportation are very important factor which control capability for responses. Due to fast transportation a life can be saved, people can be out of danger in the situation of natural calamity.

Answer:

1. This is to allow the tube of the tire to position itself properly inside the tire.

2. Inflating,deflating and reinflating aircraft tires help to eliminate all the air between the tube and the inside of the tire.

3. It helps to test the entire tube and tire assembly for any leaks.

Explanation:

Answer:

P = 7.28 N.s

Explanation:

given,

initial momentum of cue ball in x- direction,P₁ = 9 N.s

momentum of nine ball in  x-  direction, P₂ = 2 N.s

momentum in perpendicular direction i.e. y - direction,P'₂ = 2 N.s

momentum of the cue after collision = ?

using conservation of momentum

in x- direction

P₁ + p = x  + P₂

p is the initial momentum of the nine balls which is equal to zero.

9 + 0  = x  + 2

x = 7 N.s

momentum in x-direction.

equating along y-direction

P'₁ + p = y + P'₂

0 + 0 = y + 2

y = -2 N.s

the momentum of the cue ball after collision is equal to resultant of the momentum .

[tex]P = \sqrt{x^2+y^2}[/tex]

[tex]P = \sqrt{7^2+(-2)^2}[/tex]

      P = 7.28 N.s

the momentum of the cue ball after collision is equal to P = 7.28 N.s

The momentum of the cue ball after the collision is calculated to be 6.2 N·s in based on the conservation of momentum.

This physics problem involves the principle of conservation of momentum. Initially, the cue ball has a momentum of 9.0 N·s. After the collision, the nine-ball has a momentum of 2.0 N·s in the original direction and another 2.0 N·s in a perpendicular direction. To find the momentum of the cue ball after the collision, we need to take into account that the total momentum of the system is conserved before and after the collision.

In this case, the total initial momentum is the momentum of the cue ball, which is 9.0 N·s. After the collision, the total momentum should still be 9.0 N·s. The sum of the momenta of the nine-ball (which is the square root of the sum of the squares of the two momentum components, due to the Pythagorean theorem) is 2.8 N·s. Therefore, the momentum of the cue ball after the collision will be the total initial momentum minus the momentum of the nine-ball after the collision, which gives us 9.0 N·s - 2.8 N·s = 6.2 N·s.

To solve this problem, we can use the principle of conservation of momentum. Before the collision, we have the momentum of the cue ball which is 9.0 N·s. After the collision, we have the momentum of the nine-ball which is 2.0 N·s in the original direction of the cue ball and 2.0 N·s perpendicular to that direction. Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the momentum of the cue ball after the collision is the difference between the total momentum before the collision and the momentum of the nine-ball after the collision.

To calculate the momentum of the cue ball after the collision, we subtract the momenta of the nine-ball from the initial momentum of the cue ball. The momentum of the cue ball after the collision is therefore 9.0 N·s - (2.0 N·s + 2.0 N·s) = 5.0 N·s in the original direction of the cue ball.

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Answer:

0.5A

Explanation:

GIVEN THAT:

V = 3 V

R =6 ohms

V=IR

I =V/R

I = 3/6 =0.5 A

Answer:

Change, increase in note frequency of the sound that comes as a result of the reduction in the vibrating length (wavelength) when the string movement is slightly restricted at its midpoint

Explanation:

When the midpoint of a vibrating guitar string is lightly touched it reduces the wavelength of the guitar string sound, halving it and such increases the the frequency inversely by a factor of 2

The relationship

f = vw/λ, for sound wave where vw is the speed of sound, frequency, f and λ is the wavelength

Frequency varies inversely with wavelength

An Octave

is the frequency vibration of sound-wave twice that of its lower note

Answer:

[tex]f=571.67\ Hz[/tex]

Explanation:

Given:

Therefore we have the wavelength of the wave as the distance between the two consecutive maxima:

[tex]\lambda=1.2-0.6[/tex]

[tex]\lambda=0.6\ m[/tex]

We have the speed of sound in the air as:

[tex]v=343\ m.s^{-1}[/tex]

Therefore the frequency of sound:

[tex]f=\frac{v}{\lambda}[/tex]

[tex]f=\frac{343}{0.6}[/tex]

[tex]f=571.67\ Hz[/tex]

The frequency of the sound from the speaker is 571.67 Hz.

Given that the phase constant of speakers is the same, the position of one speaker is at origin, the position of another speaker from the origin is 10 m.

The position of maxima interference is at 0.6 m and 1.2 m. Hence the wavelength of the wave is equivalent to the difference between the two consecutive maxima interference.

[tex]\lambda = 1.2 - 0.6[/tex]

[tex]\lambda = 0.6 \;\rm m[/tex]

We know that the speed v of the sound in the air is 343 m/s. Hence the frequency of the sound is calculated as given below.

[tex]f = \dfrac {v}{\lambda}[/tex]

[tex]f = \dfrac { 343}{0.6}[/tex]

[tex]f = 571.67\;\rm Hz[/tex]

Hence we can conclude that the frequency of the sound from the speaker is 571.67 Hz.

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Answer:

i believe it would be classified as A shopping

Answer:

(a) 2.88×10⁻² W/m²

(b) 8.36×10⁻³ W/m²

Explanation:

The intensity of sound from an isotropic point source, with distance L is given as

I = P/(4πL²) .................................... Equation 1

Where I = intensity of sound, P = Power from the source, L = length, π = pie.

(a)

1.4 m from the source.

I = P/(4πL²)

Given: P = 0.71 W, L = 1.4 m, π = 3.14.

Substitute into equation 1

I = 0.71/(4×3.14×1.4²)

I = 0.71/24.6176

I = 0.0288 W/m².

I = 2.88×10⁻² W/m²

(b) 2.6 m from the source.

Given: P = 0.71 W, L = 2.6 m, π = 3.14

Substitute into equation 1

I = 0.71/(4×3.14×2.6²)

I = 0.71/84.9056

I = 0.00836 W/m²

I = 8.36×10⁻³ W/m²

Answer:

The value of the angle theta = 135degree, which is option c.

Explanation :

These are the options given in the question

a) 45 degrees

b)120 degrees

c)135 degrees

d)150 degrees

e) it is impossible to deliver a negative power.

The concept of work done on an object is applied here.

work = Fd

F = ma

work = mad

Work is a form of energy transferred by an object after the application of a force that act on the object. A step by step explanation is as attached below.

Answer: D. all of the above

Explanation:

The speed is important in tennis, so you can win easily, speed is important in soccer to collect the ball quickly and reach the goal, speed is necessary for swimming as the first person wins the game so, option D is correct.

A moving object's rate of change in distance traveled is measured as speed. Speed is a scalar, which implies it is a measurement with a magnitude but no direction.

A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.

Speed shortens the time needed to complete a task or travel between two locations. The spare time can then be applied to other tasks. The Earth's orbit around the Sun is maintained by speed.

Thus, speed is important in all the games mentioned here.

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Answer:

The Commemorative head of a king (Oba)

Explanation:

The commemorative head of a king is similar to the other features mentioned in the question due to their royal statuses. These features are idolized by the people in their respective societies. The 'Oba' for example is respected by the people of Benin and he makes the rules and regulations for the people. When he dies, his eldest son usually takes his position.

Answer:

The Commemorative head of a king (Oba)

Explanation:

I took the test B )

Answer: 1/2

Explanation:

The total energy consumption in the United States of America has been estimated to be about 101.3quadrillion Btu( British thermal unit). The United States of America uses a mix energy source for energy Production which includes PRIMARY, SECONDARY, RENEWABLE,FOSSIL FUELS.

Five basic energy consumption sectors have been categorized in the United States,which includes ELECTRIC POWER, INDUSTRIAL, COMMERCIAL, RESIDENTIAL AND TRANSPORTATION. Of the estimated 101.3(quads) about 1/2 of 101.3(quads) are used for the production and manufacturing of materials by the manufacturing industry.

Answer:

b. It deflects the electron to the right.

Explanation:

Since the sphere is positively charged and electron has negative charge, it will be attracted toward the sphere and hence,

The electron is deflected to the right as the positively charged sphere on its right

So, the 2nd option is correct.

Answer:

0.056 miles away

Explanation:

From sound wave,

v = 2x/t .................................. Equation 1

Where v = velocity of sound in air, x = distance of echo, t = time.

making x the subject of the equation,

x = 2v/t........................... Equation 2.

Given: v = 344 m/s, t = 7.6 s.

Substituting into equation 2

x = 2(344)/7.6

x = 90.53 m.

x = 90.53/1609.344

x = 0.056 mile.

Thus the lighting strike 0.056 miles away

Answer:

True

Explanation:

It can cause flooding and destruction of habitat because of dammed rivers create large reservoirs upstream which can spill out to the surrounding during heavy rainfall causing flooding and destruction of natural habitat.

Part A. The initial speed of the egg is 17.7 m/s.

Part B. The maximum height of the egg is 15.98 m.

Part C. The magnitude of the velocity at its highest point is 0 m/s.

Part E. The magnitude and direction of the acceleration in the upward direction is 9.8 m/s2.

Given that the distance traveled by the egg is 34 m in time 5 seconds.

The distance at its initial point will be zero.

The initial speed of the egg can be calculated by the position equation of the egg.

[tex]x = x_0 + v_0t + \dfrac {1}{2}at^2[/tex]

Where x is the initial position of the egg that is 0 m, x_0 is the final position that is 34 m in time t = 5 s, v_0 is the initial speed and a is the acceleration. Since the egg is thrown vertically, hence the acceleration of the egg is similar to the gravitational acceleration.

[tex]0 = 34 + v\times 5 + \dfrac {1}{2}\times(- 9.8)\times 5^2[/tex]

[tex]v = \dfrac {122.5 - 34}{5}[/tex]

[tex]v = 17.7 \;\rm m/s[/tex]

The initial speed of the egg is 17.7 m/s.

The maximum height for the egg can be calculated by the equation given below.

[tex]v^2 = v_0^2 + 2gh[/tex]

For the highest point, the final speed v will be zero and the initial speed v_0 is 17.7 m/s. Hence,

[tex]0 = (17.7)^2 + 2\times (-9.8)\times h[/tex]

[tex]19.6 h = 313.29[/tex]

[tex]h = 15.98 \;\rm m[/tex]

The maximum height of the egg will be 15.98 m.

The velocity of the object thrown at a height will be zero at its highest point. Hence the velocity of the egg will be zero at its highest point.

Velocity [tex]v_h[/tex] = 0 m/s

The egg is thrown vertically upward, hence its acceleration is similar to the gravitational acceleration.

Acceleration a = 9.8 m/s2

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Answer:

[tex]1.06085\times 10^{-10}\ m[/tex]

Explanation:

h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]

m = Mass of electron = [tex]9.11\times 10^{-31}\ kg[/tex]

k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]

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

n = 1 (ground state)

Angular momentum is given by

[tex]L=mvr[/tex]

From Bohr's atomic model we have

[tex]L=\dfrac{nh}{2\pi}[/tex]

[tex]mvr=\dfrac{nh}{2\pi}\\\Rightarrow v=\dfrac{nh}{2\pi mr}[/tex]

The centripetal force will balance the electrostatic force

[tex]\dfrac{ke^2}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow \dfrac{ke^2}{r}=mv^2\\\Rightarrow \dfrac{ke^2}{r}=m(\dfrac{nh}{2\pi mr})^2\\\Rightarrow r=\dfrac{n^2h^2}{4\pi^2mke^2}\\\Rightarrow r=\dfrac{1^2\times (6.626\times 10^{-34})^2}{4\pi^2 \times 9.11\times 10^{-31}\times 8.99\times 10^{9}\times (1.6\times 10^{-19})^2}\\\Rightarrow r=5.30426\times 10^{-11}\ m[/tex]

The diameter is [tex]2\times 5.30426\times 10^{-11}=1.06085\times 10^{-10}\ m[/tex]

Answer:

1- Surface water

2- Groundwater

3- Lake

4- River

5- Watershed/Catchment basin

6- Wetland

Explanation:

The questions are defining concepts involved in the study of Geography, specifically hydrology. These concepts include surface water, groundwater, a lake, a river, a watershed, and a wetland.

The series of questions relates to the nature and characteristics of different water bodies and water-related geographical phenomena.

1. Surface water refers to all liquid fresh water located above ground.
2. Precipitation that infiltrates Earth's surface and percolates downward becomes groundwater.
3. A lake is a large body of water that has extensive areas of open water, some of which is too deep for photosynthetic life.
4. A river meanders across land and structures the landscape.
5. A watershed is the entire land area that supplies a river or stream with water from precipitation.
6. A wetland has water-saturated soil, shallow standing water, and ample vegetation.

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Answer:

The acceleration of the box is 2.

Explanation:

According to Newton's second law of motion, the acceleration of any object will be directly proportional to the net unbalanced force acting on the object and inversely proportional to the mass of the object.

Net force = Mass × Acceleration

So [tex]Acceleration = \frac{Net force}{Mass}[/tex]

Since in this case, the box is experiencing a force from east of magnitude 27 N and resisting force of about 17 N from west. So the net force will be the difference of acting and reacting force.

Net force = 27-17 = 10 N.

Thus, [tex]Acceleration = \frac{10 N}{5 kg}[/tex]

So 2 [tex]m/s^{2}[/tex] is the acceleration of the box. Thus the magnitude of acceleration of the box is 2.

To find the vector sum of the electric forces exerted on particle 3, calculate the electric forces exerted by particle 1 and particle 2 and add them as vectors. Use Coulomb's law to find the electric forces. Add the x and y components of the forces to get the vector sum.

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric forces exerted on particle 3 by particle 1 and particle 2 and then add them together as vectors. The electric force exerted on particle 3 by particle 1 can be found using Coulomb's law, which states that electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

By substituting the given values into the equations, you can calculate the x and y components of the vector sum of the electric forces exerted on particle 3.

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Final answer:

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law. By plugging in the charges and distances, we can calculate the electric forces and find the vector sum.

Explanation:

To find the vector sum of the electric forces exerted on particle 3, we need to calculate the electric force between particle 3 and both particle 1 and particle 2. The electric force between two charges is given by Coulomb's Law:

F = k * (|q1| * |q2|) / r^2

Where F is the electric force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges. Since particle 1 is fixed at the origin, the distance between particle 3 and particle 1 is |-4.0 m| = 4.0 m. Similarly, the distance between particle 3 and particle 2 is |4.0 m - (-4.0 m)| = 8.0 m. Plugging in the values, we can calculate the electric forces between particle 3 and both particle 1 and particle 2.

Let's calculate:

F3-1 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (4.0 m)^2

F3-2 = (9 * 10^9 N.m^2/C^2) * (|-4.0 μC| * |8.0 μC|) / (8.0 m)^2

Now, we can find the vector sum of the electric forces by adding the x-components and the y-components of both forces.

Answer: The person will still have a mass of 90kg on Mars

Explanation: The Truth is, the mass of a body remains constant from place to place. It is the weight which is equal to {mass of body * acceleration due to gravity{g}} that varies from place to place since it is dependent on {g}.

In this case the person will have a Weight of 90*9.8 = 882N on Earth.

{ "g" on Earth is 9.8m/s²}

And a Weight of 90*3.3 = 297N on Mars.

{ From the question "g" on Mars is {9.8m/s²}/3 which is 3.3m/s²}

From this analysis you notice that the WEIGHT of the person Varies but the MASS remained Constant at 90kg.

Answer:

"Scientists used them to create new theories"

Explanation:

The Scientific Revolution was a sequence of actions that manifest the development of contemporary science through the early contemporary period, when advances in mathematics, physics, astronomy, biology and chemistry altered the opinions of civilization around nature. The scientific revolution denotes to the quick developments in European scientific, mathematical, and political assumed, grounded on a new philosophy of experimentation and a belief in growth that defined Europe in the 16th and 17th centuries.

Final answer:

The telescope and Pascal's Law played a significant role in laying the foundation of the Scientific Revolution. The telescope allowed for groundbreaking observations of the solar system and the universe, while Pascal's Law led to advancements in fluid mechanics and hydraulic engineering.

Explanation:

The new technology, such as the telescope, and new theories, such as Pascal's Law, played a significant role in laying the foundation of the Scientific Revolution.

Firstly, the invention of the telescope in 1608 allowed astronomers like Galileo Galilei to make groundbreaking observations of the solar system and the universe, leading to the development of new theories and understandings of celestial bodies.

Secondly, Pascal's Law, formulated by Blaise Pascal, established the principle that pressure exerted on a fluid is transmitted uniformly in all directions, which laid the foundation for the field of fluid mechanics and led to advancements in hydraulic engineering and other areas.

Hi you didn't provide any images to solve the question, hence I am going to solve a different question of same concept so you can have an idea how to tackle such types of questions.(please refer to the attachment for question)

Answer:

Please refer to the attachment for answers and explanation

Explanation:

Please refer to the attachment for answers and explanation

To determine the resultant internal loadings at the cross sections, we need to consider the external and internal forces. Trigonometric principles can be used to calculate the magnitudes and directions of the loadings. More information about the frame is needed for a precise analysis.

In order to determine the resultant internal loadings acting at the cross sections at points F and G of the frame, we need to consider the external forces applied to the frame, as well as the internal forces generated within the frame due to those external forces. These internal forces include axial forces, shear forces, and bending moments.

Given that θ = 27º and t = 178 lb, we can use trigonometric principles to determine the magnitudes and directions of the internal loadings at points F and G.

For a more specific and accurate analysis, it would be helpful to have more information about the frame, such as its shape, structural elements, and boundary conditions. Without that information, it is not possible to provide a more detailed answer at this time.

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Answer:

There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by

                F_hammer - F_Gravitation = m a

Explanation:

For this exercise we will propose its solution from Newton's third law, which states that every action has a reaction of equal magnitude, but felt different.

As it is in space, we must assume that it is not subject to the gravitational attraction of nearby bodies, except the asteroid that attracts it. When he extends his hand and hits the asteroid, he exerts a force on him, by Newton's third law he responds with a force of equal magnitude applied to the astronaut, therefore without the two they are not united they could separate if this force is greater than the force of universal attraction between the two.

In summary There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by

                F_hammer - F_Gravitation = m a

Answer:

3.735×10⁻⁶ N

Explanation:

From newton' s law of universal gravitation,

F = Gmm'/r² .............................. Equation 1

Where F = Gravitational force between the person and the refrigerator, m = mass of the person, m' = mass of the refrigerator, r = distance between the person and the refrigerator. G = gravitational universal constant.

Given: m = 70 kg, m' = 200 kg, r = 0.5 m

Constant: G = 6.67×10⁻¹¹ Nm²/kg².

F = (6.67×10⁻¹¹×70×200)/0.5²

F = 93380×10⁻¹¹/0.25

F = 373520×10⁻¹¹

F = 3.735×10⁻⁶ N

Hence the force between the person and the refrigerator =  3.735×10⁻⁶ N

Answer:

The work done by the force is 109.5 Joules.

Explanation:

It is given that,

Mass of the object, m = 3 kg                                

Speed of the object, v = 5 m/s

Force applied on the object, F = 12 N

Distance covered by the object, d = 6 m

The work done by this force is given by the sum of kinetic energy and potential energy as per work energy theorem as :

[tex]W=K+P[/tex]

[tex]W= \dfrac{1}{2}mv^2+Fd[/tex]

[tex]W=\dfrac{1}{2}\times 3\times (5)^2+12\times 6[/tex]

W = 109.5 Joules

So, the work done by the force is 109.5 Joules. Hence, this is the required solution.

Answer:

option (c)

Explanation:

When an object thrown upwards, the value of acceleration acting on the object is acceleration due to gravity which is always acting towards the earth.

As it falls downwards, the acceleration is again equal to the acceleration due to gravity.

So, the ball's acceleration is constant.

Final answer:

The acceleration of the ball remains constant throughout its up and down motion since it is solely influenced by gravity, which provides an acceleration of approximately 9.81 m/s² downward

Explanation:

When a ball is thrown upwards from the ground and then falls back down, the acceleration of the ball is what remains constant throughout its motion. This is due to gravity, which acts downward on the ball with an acceleration denoted as "g". While the ball's position and speed are changing throughout the motion, its acceleration due to gravity remains constant at approximately 9.81 m/s2 (on Earth), regardless of its state of motion. Therefore, the quantity that remains constant over the course of this up and down motion is the ball's acceleration.

Answer: Option (1) is the correct answer.

Explanation:

Formula to calculate correlation coefficient is as follows.

           Correlation coefficient = [tex]\sqrt{R^{2}}[/tex]

As the slope for given equation is positive so, it means that the correlation will also be positive in nature.

Therefore, we will calculate the value of correlation coefficient as follows.

         Correlation coefficient = [tex]\sqrt{R^{2}}[/tex]

                                               = [tex]\sqrt{(0.288)^{2}}[/tex]  

                                               = 0.54

Thus, we can conclude that the correlation coefficient, r is 0.54.