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?
- A.The sand exerts no reaction force.
- B.The sand reduces the change in momentum.
- C.The sand increases the impact time.
- D.The sand increases the momentum.
Correct answer
Explanation
The correct answer is C, The sand increases the impact time. Soft sand gives way slowly, so the person is brought to rest over a longer time and the force on the body is smaller.
By Newton's second law, force equals the rate of change of momentum: F = Δp / Δt. A person landing from a given height reaches the ground with a fixed momentum, and that momentum must fall to zero whatever the surface. On hard ground it falls to zero in a very short time, giving a large force that can injure. Soft sand sinks under the feet and stretches the stopping time, so the same change of momentum produces a much smaller force. Bending the knees on landing, catching a ball with the hands drawn back and airbags in cars all work the same way.
A is wrong: the sand does push back; otherwise the person would not stop.
B is wrong: the change in momentum is the same as on hard ground, from full value to zero.
D is wrong: sand does not add momentum; it brings it to zero.
Exam tip: same impulse spread over longer time means smaller force, F = Δp / Δt.
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