PART ONE
A student sits on a rotating stool holding two 5 kg objects. When his arms are extended horizontally, the objects are 0.7 m from the axis of rotation, and he rotates with angular speed of 0.75 rad/sec. The moment of inertia of the student plus the stool is 3 kg m² and is assumed to be constant. The student then pulls the objects horizontally to a radius 0.31 m from the rotation axis.
Calculate the final angular speed of the
student.
Answer in units of rad/s.

PART TWO
Calculate the change in kinetic energy of the system.
Answer in units of J.

a, b,d, g are expressions could be valid ways to calculate a distance in physics.

A physical quantity is a feature or quality of an object that may be gauged or computed from other measures. The quantification of physical quantities is expressed and evaluated using standards called units. Four fundamental units can be put together to create any unit.

The physical quantity of expression:

2πd => where d is position

d has unit 'm'

=> hence, 2πd => unit 'm'

Therefore, we can us this expression to define distance.

Sqrt (x+y ^2) => x, y are distance=> unit 'm'

=> sqrt(m+m^2) => In total, this expression does not have unit 'm'. hence, we can't use this expression to define distance.

The length, mass, time, electric current, temperature, amount of a substance, and luminous intensity are the seven fundamental physical units that constitute up the International System of Units (SI), which is used to express all physical quantities.

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Which of the following expressions could be valid ways to calculate a distance in physics? Briefly explain why/why not for each. (Hint: Think about what kind of physical quantity each term is, and what units it carries.)

(a) 2πd , where d is a position

(b) x+Δr, where x is a distance and Δr is a position difference

(c) Sqrt (x+y ^2), where x and y are both distances

(d) Sqrt( x^2+y^2), where x and y are both distances

(e) Sqrt(A+z), where A is an area and z is a distance

(f) vΔt^2, where v is a velocity and Δts a time difference

(g) aΔt^2, where a is an acceleration and Δt is a time difference

Answer:

0.0081 kg

Explanation:

A low-strength aspirin tablet contains 81 mg of the active ingredient. To find the total amount of active ingredient in a 100-tablet bottle, we can multiply the amount per tablet by the number of tablets:

81 mg/tablet * 100 tablets = 8,100 mg

To convert milligrams (mg) to kilograms (kg), we divide by 1,000,000.

8,100 mg / 1,000,000 = 0.0081 kg

So a 100-tablet bottle of baby aspirin contains 0.0081 kg of the active ingredient.

Answer:

0.0081 kg

Explanation:

number of 81 mg pills

1 kg = 106 mg

1.05005 x 105 kg = 1.05005 x 1011 mg

n = 1.5005 x 1011 / 8.1 x 10

n = 0.129635802 x 1010

n = 1.29635802 x 109

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The terminal side of an angle theta passes through the point (-6, -3) wherein x= -6 and y= -3

The six trigonometric functions of theta are as follows:

sin θ = y/r

cos θ = x/r

tan θ = y/x

cosec θ = r/y

sec θ = r/x

cot θ = x/y

wherein r= √(x^2+y^2)

Therefore, the equations become,

r= √((-6^2)+(-3^2)) = √36+9 = √45 = 6.708

hence, sin θ = (-3)/6.708 = -0.44

cos θ = (-6)/6.708 = -0.89

tan θ = (-3)/(-6) = 0.5

cosec θ = 6.708/(-3) = -2.236

sec θ= 6.708/(-6) = -1.118

cot θ = (-6)/(-3) = 2

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The velocity of the barium atom moving forward relative to the tube is 2.35 x 10^5 m/s and the velocity of the krypton atom relative to the containing tube is -2.35 x 10^5 m/s.

The velocity of the krypton atom (Kr) relative to the barium atom after separation is 2.35 x 10^5 ms^-1. This is the velocity at which the krypton atom is expected to move directly backwards after being separated from the auranium atom. It is important to note that this velocity is relative to the barium atom, and not the containing tube. To find the velocity of the krypton atom relative to the containing tube, we would need to take into account the initial velocity of the auranium atom and the mass ratios of the elements involved.

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In this process, 400 joules of work are done on the system, which means energy is being transferred into the system in the form of work. At the same time, the thermal energy of the system is decreasing by 300 joules. This suggests that the system is also losing energy in the form of heat and it indicates that the work done on the system is used to remove thermal energy from the system, leading to a decrease in the system's temperature. This process is likely an example of a cooling process, such as refrigeration or air conditioning.

Overall, the net change in the system's energy is -300 joules (decrease in thermal energy) + 400 joules (work done on the system) = 100 joules. This means that the system has gained 100 joules of energy overall, but it has gained it in the form of work and lost it in the form of heat.

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The physics professor should be 3.60m far from the physics building for the egg to successfully fall on professor's head, assuming freefall motion of the egg and acceleration to be 9.80 m/s^2.

The height of the building = 46 m

The height of the professor = 1.80 m

The effective height for freefall of the egg = 46.00 - 1.80 = 44.2 m

As S = ug + 1/2a[tex]t^{2}[/tex]

44.2 = 0 + 1/2 × [tex]t^{2}[/tex] × 9.8

[tex]t^{2}[/tex] = (2 × 44.2) / 9.8

[tex]t^{2}[/tex] = [tex]\sqrt{9.02}[/tex]

[tex]t[/tex] = 3.003 s

Let the distance travelled by the professor be x

The time taken by the egg to fall is equal to the time taken by the professor to reach the building through distance x

Speed with which the professor is walking = 1.20 m/s

Now as Distance = Speed × Time,

x = 1.20 × 3.003

x = 3.6036 meters.

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The direction of the electric force on the charge at the bottom left-hand vertex of the triangle due to the other two charges (k * q 2)/(a 2)

The amount of the charge at the triangle's top vertex, which is responsible for the charge at the bottom left corner, will act along the +ve x-axis and the +ve y-axis.

According to Coulomb's law, the forces acting on the charge at the triangle's top vertex are cos 60 and the forces acting on the charge at the bottom-left corner are

Since they resist one another, the amount of the charge caused by the charge in the bottom-right corner will only affect the -ve x-axis (like charges repel). There is a magnitude.

The top charge makes a 60° angle with the charge that we're thinking about.

F x = (k * q 2)/(a 2) * cos 60 represents the overall force acting on the charge along the x-axis.

The two x-axis forces and the y-axis force share some elements in common.

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The height of the water balloon at 10 seconds will be 0 ft.

The information for a linear pair is given in the question like ordered pair

(0,60); (2,80); (3,80); (4,20); (6,0); (7,0); (8,0)

The values (input) on the time-related x-axis make up the domain.

The values entered on the y-axis, which represents the height the balloon attained, make up the range.

Now it is given that the height of the water balloon is continuously decreasing from 3 seconds after being thrown off the roof, reaching a height of 0ft. at 6 seconds, and maintaining that height up until 8 seconds, Newton's law of motion states that at 10 seconds, provided that no additional force is applied to the balloon, its height is 0ft.

The height of 0 feet is obtained at 10 seconds after the balloon is launched by extending the graph further.

Question)- The linear model represents the height, f(x), of a water balloon...

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:

Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points)

Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer. (3 points)

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A car travels at constant speed up a hill from point A to point B. As the car travels from A to B, its gravitational potential energy (b) increases and its KE decreases.

Gravitational potential energy:

If a mass (m) moves from infinity to a point within the gravitational influence of the source mass (M) without acceleration, then in transferring it to the source field. The amount of work done is stored in the form of potential energy. This is known as gravitational potential energy. It is denoted by the symbol Ug.

We know that the potential energy of an object at a position is defined as the energy stored in the object at that position. When the position of the body changes due to the influence of an external force, the change in potential energy equals the work done by the force on the body.

Under the action of gravity, the force is conservative because the work done is independent of the path of position change. Also, all these forces have potential. Since the effect of gravity on an object at infinity is zero, it has zero potential energy, which we call the reference point.

The equation for gravitational potential energy is:

                 GPE = m × g× h

where, m is the mass in kilograms

g is the acceleration due to gravity.

h is the height above the ground in meters.

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The population in this particular problem is the pork roast. The parameter on which the population is being evaluated is 142 degrees Fahrenheit. The sample is the three random places in the pork roast where the temperature was checked. The statistic is 152 degrees Fahrenheit, which was the minimum temperature recorded during sampling.

1. The population is the object or group on which the evaluation is being done. In this scenario, the population is the pork roast.

2. Parameter is a bar which is set for measuring a feature in the population. In this problem, Micah wants the pork roast, i.e., the population, to have a minimum temperature of 142 degrees Fahrenheit.

3. A sample is chosen at random from a given population to check if the parameter matches. In this problem, Micah checked the temperature of the pork roast at three random places to deduce the average temperature of the population.

4. The statistic is the actual measurement of the sample which is compared to the parameter. In this case, the statistic would be the average minimum temperature of 152 degrees Fahrenheit.

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The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.

The conservation of linear momentum is a general law of physics which states that the overall momentum of a system is constant and that the quantity called momentum which characterises motion never changes in an isolated collection of objects.

For a system to have its momentum conserved, it must satisfy two conditions: During the interaction, the system's mass must not change. The objects may transmit mass to one another as they interact (apply forces to one another), but any mass one object gets is offset by the loss of that mass from another.

On the reasonable assumption that space is uniform—that is, that there is nothing in the rules of physics that prevents the conservation of linear momentum—the law of conservation of linear momentum is amply supported by experiment and can even be analytically inferred.

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The following are correct statements about the diagram that shows the electric field due to point charge Q:

The attraction and repulsion of electrical charges, which is what causes electric flow, create an electric field, which is an invisible force field and is measured in Volts per metre (V/m).

This question requires us to discuss what the electric field due to point charge Q is.

As a result, we can see that the electric field, which serves as the physical field that surrounds electrically-charged particles, has a nonuniform electric field and a positive charge Q.

As a result, in terms of the electric field caused by point charge Q;

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Complete question:

The diagram shows the electric field due to point charge Q. Which statements are correct? Check all that apply.

Answer:

(d) Kinetic Energy

Explanation:

Applying a force requires us to do work. After work has been done on the body, energy used by us to do work is transferred to the object, and the object will be moving with a new constant speed. The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved.

LED (light-emitting diοde) lights are the mοst efficient of the options given.

LED (light-emitting diοde) lights are the mοst efficient type of light source. They use less energy, last longer, produce less heat and are more durable than οther types of lights like incandescent, fluorescent, and sodium vapor lights.

They are also more energy-efficient and ecο-friendly.

They use less energy than incandescent and fluοrescent lights.

They have a lοnger lifespan than incandescent and fluorescent lights.

They produce less heat than incandescent and fluοrescent lights.

They are more durable and mοre resistant to breakage than incandescent and fluοrescent lights.

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The best design for testing whether memory is accurate would be option C: Experimental design.

An experimental design allows the researcher to manipulate one or more independent variables and observe the effect on a dependent variable, in this case, memory accuracy.

This type of design allows for a cause-and-effect relationship to be established, as the manipulation of the independent variable is the only reason for the change in the dependent variable. This design also allows the researcher to control for extraneous variables that could affect the results.

In conclusion, an experimental design is the best option for testing whether memory is accurate as it allows for a cause-and-effect relationship to be established, allows the researcher to control for extraneous variables and allows for generalizing the findings to a larger population.

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Kinetic energy reaches its peak at the track's lowest point as the skater goes back and forth.

In physics, an object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a given velocity. The body retains its kinetic energy after gaining it during acceleration unless its speed changes. Kinetic energy is the energy of motion, which can be seen as an object or subatomic particle moving. Kinetic energy exists in every moving object and particle. Kinetic energy is demonstrated by a person walking, a soaring baseball, a crumb falling from a table, and a charged particle in an electric field.

Here,

Kinetic energy peaks at the lowest point of the track as the skater goes back and forth.

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a. The tension in the string in the equilibrium position is 980 N.

In the equilibrium position, the bob is simply hanging and is not moving, so the net force on the bob is 0. The force acting on the bob is the tension in the string, which is equal to the weight of the bob (mg) in the opposite direction.

Therefore, the tension in the string in the equilibrium position is equal to the weight of the bob, which is [tex](100g)(9.8 m/s^2) = 980 N[/tex].

b. The height to which the bob is raised is 0.063 m.

It can be calculated using the equation h=L(1-cos theta).

Therefore, the angle theta is 18 degrees, so the height is (2m)(1-cos 18) = 0.063 m.

c. The potential energy gained in the process is 6.1 J

It can be calculated using the equation PE = mgh. The mass of the bob is 100g = 0.1 kg, the height is 0.063 m and the acceleration due to gravity is 9.8 m/s^2.

Therefore, the potential energy is [tex](0.1 kg)(9.8 m/s^2)(0.063 m)[/tex] = 6.1 J.

d. The velocity with which the bob moves past the equilibrium position is 4.5 m/s.

It can be calculated using the equation [tex]v = \sqrt{ (2gL)[/tex] The acceleration due to gravity is [tex]9.8 m/s^2[/tex] and the length of the pendulum is 2 m, so the velocity is [tex]\sqrt (2(9.8 m/s^2)(2m))[/tex] = 4.5 m/s.

e. The tension in the string as the bob moves past the equilibrium position is 24.7 N.

It can be calculated using the equation [tex]T - mg = mv^2/r[/tex]. The mass of the bob is 100g = 0.1 kg, the velocity is 4.5 m/s, and the radius is 2m, so the tension is [tex](0.1 kg)(4.5 m/s)^2/(2m) + (0.1 kg)(9.8 m/s^2)[/tex] = 24.7 N.

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When an object's location varies over time, it is said to be in motion. Motion is defined by the six variables displacement, distance, velocity, acceleration, time, and speed.

What exactly did you mean by "motion"?

Motion in physics changes over time depending on the location or orientation of a body. The action of travelling along a straight or curved line is known as translation. The term "rotation" refers to motion that changes the orientation of a body. The act or process of moving, or even the passage of a body from one point to another, is referred to as movement.

The act of moving one's body or any of its parts. 3. an intentional movement of the hand, gaze, etc.

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The scale reading is actually a measure of the upward force applied by the scale to balance the downward force of gravity acting upon an object

Scales measure weight, which is the force acting on a mass equal to the mass times the acceleration of gravity of the object. Due to the dependence of the weighing mechanism and the weight of any given object on the local gravity, a scale cannot accurately determine mass.

Although we use a scale to determine how much we weigh, the scale reading actually represents the upward force the scale applies to an object to counteract the downward force of gravity. These two forces are balanced when an object is in an equilibrium condition (whether it is at rest or moving at a constant speed).

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The quantity of water used, the type of spaghetti used, and the intervals at which the spaghetti is checked to see if it is finished.

Water becomes harder due to the presence of calcium, magnesium, and iron(II) ions, which prevents soap solution from creating a lather. Students examine the impact of several dissolved salts, which comprise a variety of cations and anions, on the production of lather in this experiment. After that, they try to determine which ions are impeding lathering.

The students can work in pairs or bigger groups to complete this as a class project.

The first step for the students is to label eight test tubes. Alternatively, they can individually conduct an investigation using three or four more test tubes and distilled water, as long as they include at least one sodium or potassium salt and one calcium or magnesium salt.

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The slope of the resulting line can be referred to as the viscosity.

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(a) Impulse delivered to the ball by the floor is 3.8 kg.m/s, and direction is upward. (b) average force exerted on the ball by the floor is 95 N, and the direction is upward.

Amount of force applied for a certain amount of time to cause the change in momentum is called impulse.

(a) impulse delivered to ball by the floor is;

As, impulse = change in momentum = m(vf - vi)

where m is  mass of the ball, vf is  final velocity of the ball after the collision and vi is  initial velocity of the ball before collision.

Since the ball falls from a height of 18.5 m and rebounds to a height of 15.0 m, we know that the final velocity of the ball is upward, and the initial velocity of the ball is downward.

final velocity ; vf = sqrt(2gh)

where g is acceleration due to gravity and h is height of the rebound.

initial velocity; vi = sqrt(2gh)

where g is acceleration due to gravity and h is height of the fall.

vf = sqrt(29.815) = 7.68 m/s

vi = sqrt(29.818.5) = -10.26 m/s (upwards)

So, impulse = m(vf - vi) = 0.360 kg * (7.68 m/s - (-10.26 m/s)) = 3.8 kg.m/s

The impulse delivered to the ball by the floor is 3.8 kg.m/s, and direction is upward.

(b) The average force exerted on the ball by the floor;

average force = impulse / time of contact = 3.8 kg.m/s / 0.0400 s = 95 N

direction of force is upward.

The average force exerted on the ball by the floor is 95 N, and the direction is upward.

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The viscosity of the solution i.e. the value of D in the equation is 0.045 [tex]kgm^{-1} s^{-1}[/tex] or 0.045 newton-second per square meter.

At time t = 0,

y(t) = A + Bt + C[tex]e^{-Dt}[/tex]

0.07 = A + C    (as t = 0 and power of zero gives unity)  

y component of v at t = 0 => [tex]\frac{dy}{dt}[/tex] = 0

=> 0 + B + (-D) C[tex]e^{-Dt}[/tex] = 0

=> B - CD = 0  

=> B = CD         (as t = 0 and power of zero gives unity)  

y component of acceleration a at t = 0 => [tex]\frac{dv}{dt}[/tex] = 0.025

=> 0 - (-D)CD[tex]e^{-Dt}[/tex] = 0.025

=> C[tex]D^{2}[/tex] = 0.025 (as t = 0 and power of zero gives unity)  

At time = ∞

y component of velocity v => 0 + B + (-D) C[tex]e^{-Dt}[/tex] = 0.55

=> B = 0.55       (as t = ∞ and power of  ∞ gives 0)

Now, using B = 0.55, CD = 0.55

As C[tex]D^{2}[/tex] = 0.025 => 0.55 × [tex]D[/tex] = 0.025

=> [tex]D[/tex] = 25 / 550 = 0.045

Hence, the viscosity of the solution is  0.045 [tex]kgm^{-1} s^{-1}[/tex] or 0.045 newton-second per square meter.

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620V current I3, Electric circuits can be simple or sophisticated, but they all consist of the same three fundamental parts:

V = I * R = 31.00 * 20.00 = 620V.

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The NEE directional component is quite consistent throughout the year, with the exception of the summer months.

The wind direction from NEE is more frequent in the winter and spring, when cold air masses dominate the region.

The other predominant direction from which the wind blows is the Southwest (SW). The percentage of time that the wind blows from the SW is approximately 31%. The SW directional component is quite consistent throughout the year, and tends to be more frequent in the summer and fall months. This direction of wind is usually associated with warm air masses, which can bring rainfall and storms.

The remaining wind directions, from the North (N), South (S), East (E), and West (W), make up the remaining 32-33% of the time. These directions are usually associated with different weather patterns and are more variable throughout the year. For example, during the summer months, the N and S directional components will be higher than the E and W directional components.

The variability in wind direction throughout the year is caused by a combination of large-scale weather patterns and local terrain. The large-scale weather patterns that affect wind direction are the prevailing winds and global circulation patterns. Local terrain also plays a role, as some areas may have more of a particular direction of wind due to their location.

Overall, the NEE and SW directions are the most predominant wind directions in the region. Although the other four directions make up the remaining portion of the wind patterns, they are usually associated with different weather patterns and are more variable throughout the year.

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The distance traveled by the sperm whale traveling at an initial speed of 1.10m/s to 2.44m/s is 23.7m.

The distance traveled by the sperm whale can be estimated using one of the equations of motion as follows:

v² = u² + 2as

Where;

According to this question, a sperm whale can accelerate at about 0.100 m/s² when swimming on the surface of the ocean. The distance traveled by the whale can be calculated as follows:

2.44² = 1.10² + 2(0.10)(s)

5.95 = 1.21 + 0.2s

4.74 = 0.2s

s = 23.7m

Therefore, 23.7m is the distance of the sperm whale.

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The magnitude of the force is directly related to the amount of work done; the greater the force, the greater the amount of work done on the particle.

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Velocity is a vector quantity that describes an object's change in position over time. The general definition of velocity is the derivative of the position vector ~r with respect to time, denoted as v = dr/dt. This means that velocity is the rate of change of position with respect to time. It is also a measure of how fast an object is moving in a particular direction.

Acceleration is another vector quantity that describes an object's change in velocity over time. The general definition of acceleration is the derivative of the velocity vector ~v with respect to time,

denoted as a = dv/dt. This means that acceleration is the rate of change of velocity with respect to time. It is also a measure of how quickly an object's velocity is changing.

In summary, velocity is a measure of how fast an object is moving in a particular direction, while the acceleration is a measure of how quickly an object's velocity is changing. Both are vector quantities and can be described in terms of position vector ~r.

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Answer:help

Explanation:i help

29.69 J is the gravitational potential energy of the softball at its highest position.

29.69 J is the kinetic energy of the softball when it returns to your hand.

14.069 m/s is the speed of the ball.

The energy of motion, or kinetic energy, may be seen in the movement of an item or subatomic particle. Kinetic energy can be discovered in every moving object and particle. Kinetic energy is generated when anything moving, such as a person walking, a baseball rising through the air, a piece of food dropping from a table, or a charged particle in an electric field. The object's squared velocity determines the kinetic energy. As a result, an object's kinetic energy quadruples when its velocity doubles.

Kinetic energy is divided into five kinds radiative, thermal, sound, electrically, and mechanic.

given that,

mass of the ball = 300 g = 0.3 Kg

maximum altitude of the ball = 10.1 m

Potential energy of the softball:

P.E = mgh

P.E = 0.3 x 9.8 x 10.1

P.E = 29.69 J

Maximum kinetic energy at which the ball is released from hand to reach height of 10.1 m is 29.69 J.

Kinetic energy at which ball returns to your hand is equal to 29.69 J.

speed of the ball:

K.E = 1/2 mv²

or, 29.69 = 1/2 × 0.3 × v²

or, v² = 197.93

or, v = 14.069 m/s

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