A 65 kg person jumps from the first-floor window of a burning building and lands

Question

A 65 kg person jumps from the first-floor window of a burning building and lands almost vertcially on the ground with a horizontal velocity of 3 m/s and vertical velocity of -9 m/s. Upon impact with the ground he is brought to rest in a short time. The force experienced by his feet depends on whether he keeps his knees stiff or bends them. Find the force on his feet in each case.

A) First find the impulse on the person from the impact on the ground. Calculate both its magnitude and direction.

B) Find the average force on the feet if the person keeps his leg stiff and straight and his center of mass drops by only 1 cm vertically and 1 cm horizontally during the impact.

C) Find the average force on the feet if the person bends his legs throughout the impact so that his enter of mass drops by 50 cm vertically and 5 cm horizontally during the impact.

D) Compare the results of part (b) and (c), and draw conclusions about which way is better.

Explanation / Answer

A) impulse by ground = - mv = 65*sqrt (9^2 +3^2)

= 617 kg m/s

Direction =arctan (9/3) = 108 degree above horizontal in forward or 72 degree above horizontal from backward.

B) Force = mv^2/2s = 65*9^2/(2*0.01) j - 65*3^2/(2*0.01) i

= 263250 j - 29250 i N

= sqrt (263250^2 +29250^2)

= 264870 N

C) Force =mv^2/2s = 65*9^2/(2*0.50) j - 65*3^2/(2*0.05) i

= 5265 j - 5850 i N

= sqrt (5265^2 +5850^2)

= 7870 N

D) part c way is better as less force will be exerted on the feet.

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