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 71 m. He was propelled inside the barrel for 5.4 m and launched at an angle of 52°. If his mass was 86 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 52°. Neglect air drag.)

571.04 N

Step-by-step explanation:

First we calculate the velocity with which he is ejected from the cannon. Using the formula for the range ,R of a projectile, R = U²sin2θ/g

So, U = √(gR/sin2θ)

g = 9.8 m/s², R = 71 m, θ = 52°

U = √(9.8 × 71 ÷ sin(2 × 52°) ) = √(695.8/sin104°) = √(695.8/0.9703) = √717.101 = 26.779 m/s ≅ 26.78 m/s

Since Emanuel Zacchini was shot from rest in the barrel of length 5.4 m, we calculate his acceleration in the barrel using v² = u² + 2as. Since u = 0, v = 26.78 m/s and s = 5.4 m, a = (v² - u²)/2s = (26.78² - 0)/(2× 5.4) = 717.1684/108 = 6.64 m/s². The force on him for this acceleration is given by F = ma , m = 86 kg, a = 6.64 m/s². So, F = 86 × 6.64 = 571.04 N ≅ 571 N

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