The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: . We can rewrite this equation in terms of force.

Using this transformation, we can see that momentum is also equal to force times time.

  can also be thought of as .

Expand this equation to include our given values.

Since the object is not moving at the end, its final velocity is zero. Plug in the given values and solve for the force.

We would expect the answer to be negative because the force of friction acts in the direction opposite to the initial velocity.

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: . We can rewrite this equation in terms of force.

Using this transformation, we can see that momentum is also equal to force times time.

 can also be thought of as .

Expand this equation to include our given values.

Since the box is not moving at the end, its final velocity is zero. Plug in the given values and solve for the time.

The problem tells us he falls vertically off the ladder (straight down), so we don't need to worry about motion in the horizontal direction.

The equation for momentum is:

We can assume he falls from rest, which allows us to find the initial momentum.

.

From here, we can use the formula for impulse:

We know his initial momentum is zero, so we can remove this variable from the equation.

The problem tells us that his change in time is s seconds, so we can insert this in place of the time.

The only force acting upon man is the force due to gravity, which will always be given by the equation .

In both cases the egg starts with the same velocity, so it has the same initial momentum. In both cases the egg stops moving at the end of its fall, so it has the same final velocity. The only thing that changes is the time and force of the impact. The force is produced by the deceleration resulting from the time that the egg is in contact with its point of impact.

As the time of contact increases, acceleration decreases and force decreases.

As the time of contact decreases, acceleration increases and force increases.

The grass will have less force on the egg, allowing for a lesser acceleration, due to a longer period of impact.

The change in momentum is the final momentum minus the initial momentum, or .

Notice that the problem gives us the final SPEED of the ball but not the final VELOCITY. Since the ball "bounced back," it begins to move in the opposite direction, so its velocity at this point will be negative.

Plug in our values to solve:

If we were to examine the area under the curve of a constant force applied over a certain amount of time we would have a graph with a straight horizontal line.  To find the area of that rectangle we would multiply the base times the height.  The base would be the time (number of seconds the force was applied).  The height would be the amount of force applied during this time.  Force*time is equal to the impulse acting on the object which is equal to the change in momentum of the object.

We know that if the balls fell straight down after the crash, then the total momentum in the horizontal direction is zero. The only motion is due to gravity, rather than any remaining horizontal momentum. Based on conservation of momentum, the initial and final momentum values must be equal. If the final horizontal momentum is zero, then the initial horizontal momentum must also be zero.

In our situation, the final momentum is going to be zero.

Use the given values for the mass of each ball and initial velocity of the first ball to find the initial velocity of the second.

The negative sign tells us the second ball is traveling in the opposite direction as the first, meaning it must be moving east.

The impulse is equal to the change in momentum. The change in momentum is equal to the mass times the change in velocity.  

The yellow ball rebounds higher and therefore has a higher velocity after the rebound.  Since it has a higher velocity after the collision, the overall change in momentum is greater.  Therefore since the change in momentum is greater, the impulse is higher.

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy. 

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for .

The total momentum before the collision is equal to the momentum of each object added together.

Remember that moving to the left means that the object has a negative velocity

Total momentum = 

According to the law of conservation of momentum, the total momentum at the end must equal the total momentum at the beginning.  Since the momentum at the beginning was , the momentum at the end would also be .