Question

In February 1955, a paratrooper fell 370 m from an airplane without being able to open his chute but happened to land in snow, suffering only minor injuries. Assume that his speed at impact was 56 m/s (terminal speed), that his mass (including gear) was 85 kg, and that the magnitude of the force on him from the snow was at the survivable limit of 1.2×10⁵N.

What are (a) the minimum depth of snow that would have stopped him safely and (b) the magnitude of the impulse on him from the snow?

Answer 1

(a) 1.11 m

(b) 4760 kgm/s

Step-by-step explanation:

height of plane (h) = 370 m

velocity (v) = 56 m/s

mass (m) = 85 kg

force = 1.2 x 10^{5} N = 120,000 N

(a) We can get the minimum depth of snow from the equation below

force x depth = kinetic energy on impact

f x d = 0.5 x m x v^{2}

120000 x d = 0.5 x 85 x 56^{2}

d= (0.5 x 85 x 56^{2}) ÷ 120000 = 1.11 m

(b) the magnitude of impulse is equal to the momentum of the paratrooper and his gear

= m x v

= 85 x 56 = 4760 kgm/s