Q63 / 270 · NDA 2026 (Phase 1) · General Ability
A person jumps from a height on soft sand. Which one of the following is the correct reason for less likely injury to the person?
- AThe sand exerts no reaction force.
- BThe sand reduces the change in momentum.
- Correct answerCThe sand increases the impact time.
- DThe sand increases the momentum.
Solution
According to Newton's second law of motion, the average force exerted on a body is equal to the rate of change of momentum, $F = \dfrac{\Delta p}{\Delta t}$.
When a person jumps from a height onto soft sand, the sand yields under the person's weight. This increases the time of impact $\Delta t$ for the person to come to rest.
Since the change in momentum $\Delta p$ remains the same (as the initial velocity just before impact and the final velocity of zero are unchanged), an increase in the impact time $\Delta t$ results in a significant decrease in the average force $F$ exerted on the person.
A smaller force reduces the likelihood of injury. Therefore, the soft sand increases the impact time.
When a person jumps from a height onto soft sand, the sand yields under the person's weight. This increases the time of impact $\Delta t$ for the person to come to rest.
Since the change in momentum $\Delta p$ remains the same (as the initial velocity just before impact and the final velocity of zero are unchanged), an increase in the impact time $\Delta t$ results in a significant decrease in the average force $F$ exerted on the person.
A smaller force reduces the likelihood of injury. Therefore, the soft sand increases the impact time.
Hence, the correct answer is option: 'C'.