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?

Question

Physics

William Hunt

23 January, 22:33

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?

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Answers (1)

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Tabitha Chen · Answer 1

(a) 1.11 m

(b) 4760 kgm/s

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