Use conservation of momentum

Plug in values:

Solve for :

The average force exerted by the racket is related to the impulse by

The impulse is related to the change in momentum by 

Equating the two expressions for impulse gives us 

Simplify to get

The change in velocity  is given as 

Plugging in this, along with the given change in time and mass of the tennis ball gives us:

Since the question asks for the magnitude of the average force, we get rid of the negative above to obtain 

Use the equation for momentum:

Initial velocity was

Plug in values:

We need to use the equation for impulse to solve this problem. In fact, the time given is completely irrevelevant:

Plugging in our values:

This is less than the threshold, so no, nothing becomes structurally compromised

In order to determine the momentum of the arrow, we are going to need its velocity at that time. First, we will convert the initial kinetic energy into initial velocity:

Rearranging for velocity:

Then we can use the following equation to calculate the velocity after 1 second:

Then using the expression for momentum:

Momentum is conserved in isolated systems, (i.e. there are no net external forces.)

Using the equation for kinetic energy

Converting to and plugging in values:

Using momentum principle:

Since the cars have identical masses and experience the same change in velocity, the forces on them will be identical.

Plugging in values:

Solving for :

Using momentum principle:

Since the cars have identical masses and experience the same change in velocity, the forces on them will be identical.

Plugging in values:

Solving for :

Now, determine the acceleration of the car:

Now, determine the force experienced by the driver who was in the car, and thus accelerated with the car.

For this question, we're asked how a padded landing helps a person fall safely from a large height. To do so, we need to consider how the landing interacts with the falling person in changing their momentum.

Let's first remember that a change in an object's momentum is called impulse, which can be written with the following expression.

What's more, the units can be rearranged in such a way as to express impulse in terms of average force and time of the collision.

Next, we can rearrange the above expression to make it easier to see how force and time of collision are related.

As we can see in the above expression, the average force of collision is inversely proportional to the time of the collision. In other words, the longer the collision lasts, the less the average force will be.

Relating this to the padded landing example, it's clear that the landing helps to reduce a person's fall by reducing the average force of the collision between the person and the landing. Moreover, the amount of time the collision takes to happen is increased.