A high-jumper, having just cleared the bar, lands on an air mattress and comes to rest. Had she landed directly on the hard ground, her stopping time would have been much shorter. Using the impulse-momentum theorem as your guide, determine which one of the following statements is correct.

The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. Momentum is calculated by multiplying an object's mass by its velocity, while impulse is calculated by multiplying force by time.

In this scenario, we can compare the landing on the air mattress to the landing on the hard ground to determine the correct statement.

When landing on the air mattress, the time of contact between the jumper and the mattress is longer compared to the hard ground. As a result, the time of deceleration is greater, leading to a longer time interval over which the jumper's momentum changes.

According to the impulse-momentum theorem, if the time taken for an object to change its momentum is longer, the average force applied is smaller. Conversely, if the time is shorter, the average force is larger.

Therefore, the correct statement is: "The stopping force acting on the jumper when landing on the air mattress is smaller compared to landing directly on the hard ground."

The impulse-momentum theorem states that the change in momentum is equal to the impulse applied to an object. In this scenario, let's assume that the momentum of the high-jumper before landing on the air mattress is the same as the momentum she would have had if she had landed directly on the hard ground.

Now, let's consider the two scenarios:

1. Landing on the air mattress:
When the high-jumper lands on the air mattress, the impulse exerted on her is spread out over a longer time period, resulting in a longer stopping time. Since the impulse is the same as in the other scenario, but the stopping time is longer, the change in momentum is smaller.

2. Landing on the hard ground:
If the high-jumper were to land directly on the hard ground instead, the impulse exerted on her would be spread out over a shorter time period, resulting in a shorter stopping time. Since the impulse is the same as in the previous scenario, but the stopping time is shorter, the change in momentum is greater.

Based on the impulse-momentum theorem, we can conclude that the correct statement is:

- If the high-jumper had landed directly on the hard ground, her stopping time would have been much shorter.

The air mattress exerts the same impulse, but a smaller net average force, on the high-jumper than does the hard ground.