The Zacchini family was renowned for their humancannonball act in which a family

Question

The Zacchini family was renowned for their humancannonball act in which a family member was shot from a cannon using either elastic bands or compressed air. In one version of the act, Emanuel Zacchini was shot over three Ferris wheels to land in a net at the same height as the open end of the cannon and at a range of 68 m. He was propelled inside the barrel for 5.7 m and launched at an angle of 50°. If his mass was 81 kg and he underwent constant acceleration inside the barrel, what was the magnitude of the force propelling him? (Hint: Treat the launch as though it were along a ramp at 50°. Neglect air drag.)

Explanation / Answer

First, use the formula for range of a projectile

R = vo2sin(2angle)/g

68 = vo2(sin 100)/(9.8)

v = 26.01 m/s2

Then we can find the acceleration in the barrel

vf2 = vo2 + 2ad

26.012 = 0 + 2(a)(5.7)

a = 59.4 m/s2

Finally apply F = ma

F = (81)(59.4) = 4808 N

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