Question

A paratrooper whose chute fails to open lands in snow; he is hurt slightly. Had he landed on bare ground, the stopping time would have been 10 times shorter and the collision lethal. Does the presence of the snow increase, decrease, or leave unchanged the values of (1) the paratrooper’s change in momentum, (2) the impulse stopping the paratrooper, and (3) the force stopping the paratrooper?



A paratrooper whose chute fails to open lands in snow; he is hurt slightly. Had he landed on bare ground, the stopping time would have been 10 times shorter and the collision lethal. Does the presence of the snow increase, decrease, or leave unchanged the values of (1) the paratrooper’s change in momentum, (2) the impulse stopping the paratrooper, and (3) the force stopping the paratrooper?

A
(1) increase; (2) unchanged; (3) decrease;

B
(1) unchanged; (2)increase; (3) decrease;

C
(1) unchanged; (2) unchanged; (3) decrease;

D
(1) unchanged; (2) unchanged; (3) increase

Answer 1

Answer:

C

Explanation:

Change in momentum would be the mass of the paratrooper x his change in velocity. This is independent of the time taken.

$\Delta p = m v$

His impulse would not change either. Impulse is average force x time or change in momentum x time. Since the snow prolongs the time of impact, it would increase the time duration which the force is acting in. Since the impulse is the same and the time duration increases, the force on the paratrooper when he lands would decrease.

$I = F_{av} \x t\\I = const\\\rightarrow F \propto\frac{1}{t}$

where I = impulse, F = average force and t = time of impact

This is why it's less injurious to fall into water than on concrete from a low height and so on. There are many everyday examples.