Use work:

All energy will be kinetic.

Convert to :

Plug in values. Force will be negative as it is directed against the direction of travel:

Solve for :

Converting to

We first need to find the net force acting on the ball during flight. We can then use the net force and Newton's second law to find the total acceleration on the ball.

Use this net force to find the acceleration.

From here, there are two ways to solve. One way uses kinematic equations, and the other uses energy. We will solve using energy.

Total energy must be conserved during the throw, so the initial kinetic energy must equal the final potential energy (since velocity is zero at the maximum height).

Use the given initial velocity to find the final height.

For this question, we're told that an object is normally lifted a certain vertical distance. However, a ramp is to be added in order to make it easier to lift the object to the desired position, and we're asked to find out how much easier it will be by determining how the force required to lift it will change.

First, we must approach this problem from the perspective of energy. Specifically, we need to look at the change in gravitational potential energy. When the object is lifted a certain distance, its gravitational potential energy will increase according to the following expression:

Furthermore, it's important to realize that the change in mechanical potential energy only cares about the final and initial positions; it does NOT care about the path taken to get from initial to final. Therefore, the change in mechanical potential energy for lifting the object directly up is exactly the same as if the object were to be moved up a ramp to the same vertical location.

What's more is that we can realize the gravitational potential energy will be increasing as it is lifted, thus we need to put energy into this process by doing work. We can write the expression for work as follows:

Since the amount of work done on both processes is the same, we can set the two expressions equal to each other as follows:

By rearranging, we obtain:

The expression shown above tells us how the force needed to transfer the object via the ramp is different from the force needed to lift the object directly.

Thus, the force needed to move the object via the ramp is halved compared to the original force. Essentially, since we doubled the distance, we halved the force.

The answer is because no work is done. For work to be done a force must be exerted across a distance parallel to the direction of the force. In this case, a force is exerted by the man but the wall is stationary and since it does not move there is no distance for work to take place on. The formula for work can be written as:

Here, is zero, so is also zero, making the entire term, and thus the work zero.

Based on the information given, his throw would have started at above the ground. The pizza gained a maximum height of . Thus, the gravitational potential energy in relation to the starting position will be:

Since at it's maximum height, all of the energy will be gravitational, the work done on the pizza will be equal to the potential energy, thus:

Using

Using the equation of momentum,

we can compare the initial and final scenarios and set them equal to each other to solve for the final velocity of the block (don't forget to convert the units of to !):

First let's draw a free body diagram of the block with all the forces acting on it.

The block has a weight force which is . The normal force is equal and opposite (otherwise the block would be accelerating into the ground or into the air. The applied force is at an angle, and in order to find the work done we need to find the applied force that is pulling the block across the floor. This is:

The work done is just the product of the applied force and the distance the block slides,

Work is an energy, and the units of are equal to Joules.

Use the definition of work:

Plug in known values and solve.

This can be a tricky question. You need to rely on the work-energy theorem, which states:

Since the elevator is at rest at both the beginning and end, the net work is 0; there is no net change in energy, and therefore no work.

This theorem can be confusing to some since it completely negates potential energy. However, let's think about the situation presented in the problem. A force is required to raise the elevator, meaning that energy is put into the system. However, since it comes back to rest, all of the energy that was put in has been removed by the force of gravity, resulting in a net of zero work.