The first thing we need to find is the final velocity of the car. We know it starts from rest and has an acceleration of for five seconds. We can calculate the final velocity using these values and the appropriate kinematics equation.

The formula for kinetic energy is:

We can use the calculated final velocity and the mass of the car to determine its final kinetic energy.

To find average power, we find the total work done by the crane in lifting the steel beam, and then divide it by the time taken to complete the task.

In this case, the total work done is equal to the change in potential energy of the steel beam. for this, we use the potential energy equation:

We then divide the work by  to find average power:

A perfectly inelastic collision is when the two bodies stick together at the end. At the beginning the two balls are traveling separately with individual momentum values. Using the momentum equation , we can see that ball A has a momentum of (4kg)(7m/s) to the right and ball B has a momentum of (6kg)(8m/s) to the left. The final momentum would be the mass of both balls times the final velocity, (4+6)(v_f). We can solve for v_f through conservation of momentum; the sum of the initial momentum values must equal the final momentum.

Note: ball B's velocity is negative because they are traveling in opposite directions.

The negative sign indicates the direction in which the two balls are traveling. Since the sign is negative and we indicated that traveling to the left is negative, the two balls must be traveling 2m/s to the left after the perfectly inelastic collision.

Apply conservation of momentum before and after the collision.

.

Taking left to be the negative direction, and noting that Bob's initial momentum is 0 since he is at rest, we can use the provided information to see that  .

Solving for , we get . Since this answer is positive, Bob's momentum is in the positive direction (to the right).

The law of gravitation is written as , with G being equal to .

Since the radius of the two masses acting on each other is squared, and is found in the denominator, a decrease in the radius by a multiple of three will cause a nine-fold increase in the gravitational force.

Solve the following equation for acceleration, using the values given in the question.

First we can calculate the acceleration.

Using F = ma with the magnitude of the acceleration we can find the force.

In order to calculate the change in momentum, we must find the initial and final momentum of the baseball, and then find the difference.

Use the given velocities and mass to calculate the initial and final values.

The initial momentum is positive because the problem states that the ball was originally thrown in the positive direction. The final momentum is negative due to the change in direction.

Now we find the change in momentum:

Since the box is moving when the net force on the box is determined, we can calculate the coefficient of kinetic friction for the box. The first step is determining what the net force on the box would be in the absence of friction. The net force on the box is given by the equation .

The difference between the frictionless net force and the net force with friction is 0.8N. This means that the force of kinetic friction on the box is 0.8N, acting opposite the direction of motion. Knowing this, we can solve for the coefficient of kinetic friction using the equation 

The most important part of this question is noticing that it asks how much work has been done on the bar, not how much work the bodybuilder has exerted. Therefore we can use the work energy theorem:

Since the bar is initially at rest and returns to rest, the net work on the bar is zero. All of the energy exerted by the bodybuilder is counteracted by gravity.

Think about the system practically. Comparing the initial and final states, the bar is in the exact same position.