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Terminal velocity of pilot; ideal pulley; pop gun's spring

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1. In 1955 a pilot fell 370 meters without his parachute opening. He landed in a snowbank, making a crater 1.1 meters deep. He walked away with minor injuries. If his mass was 80 kg and his terminal velocity was 35 m/s, calculate

a) the work done on him by the snow
b) the average force exerted on him by the snow
c) the work done on him by air resistance

2. An ideal pulley has a string over it, with masses attached to either end. One end has a 5kg mass, sitting on the floor. The other end has an 8kg mass, which starts from rest but the string is so short that it starts 3 meters above the floor. Use the work-energy theorem to calculate the masses' speeds when the 8kg mass reaches the floor

3. My 'pop' gun is essentially a spring that fires marbles as projectiles. If I load the gun by compressing the spring 9cm with 7 newtons of force, how fast will it project a 25 gram marble?

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Solution Preview

Problem 1.

The physics you need to apply to this problem is that energy is changed from one form to another. If potential energy PE is lost then energy appears in some form(s) in equal quantity.
Let M= 80 kg, H= 370 m, D= 1.1 m, and v= 35 m/s.
Part a1. In moving distance D into the snow in coming to rest: Work done by snow = PE lost in snowbank + KE lost in stopping
W= M g D + .5 M v^2 = (80 kg)(9.8 ...

Solution Summary

The terminal velocity of a pilot is provided so the expert can calculate the work done on him by the snow, the average force exerted on him by the snow and the work done by air resistance.