Increase the time duration of the impact to reduce the force.
Explanation
The scenario is governed by Newton's Second Law of Motion and the concept of Impulse. According to Newton's Second Law, the force exerted on a body is equal to the rate of change of its momentum ($F = \frac{\Delta p}{\Delta t}$). Impulse is the product of force and the time duration over which it acts ($J = F \times \Delta t$).
Detailed Analysis
When a high jumper lands, their velocity is brought to zero. The total change in momentum ($\Delta p$) is determined by the athlete's mass and velocity just before impact. This value remains constant regardless of the surface they land on.
- Decrease the total change in momentum of the athlete. is Incorrect: The total change in momentum is fixed because the athlete must come to a complete stop from a specific velocity. The landing surface does not alter the initial or final momentum states, only how that change occurs.
- Increase the time duration of the impact to reduce the force. is Correct: A cushioned bed or sand bed is soft and yields under the athlete's weight. This deformation increases the time duration ($\Delta t$) taken for the athlete to come to rest. Since Force is inversely proportional to time for a constant change in momentum ($F = \frac{\Delta p}{\Delta t}$), increasing the time interval significantly reduces the impact force experienced by the athlete, thereby preventing injury.
- Increase the reaction force exerted by the ground. is Incorrect: The objective of using a cushioned bed is to decrease the reaction force exerted by the ground on the athlete, not increase it. A higher reaction force would cause injury.
- Reduce the gravitational pull on the athlete. is Incorrect: The gravitational pull on the athlete depends on the athlete's mass and the Earth's gravity ($g$). The nature of the landing surface has no effect on gravitational force.
Key Takeaway: To minimize impact force during a collision or fall, one must extend the time interval over which the momentum changes. This is the same principle used in seatbelts, airbags, and catching a cricket ball by pulling hands backward.