At the start of his race, 86-kg Olympic 100m champion Usain Bolt pushes against the starting block, exerting an average force of

Question

2 years ago

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At the start of his race, 86-kg Olympic 100m champion Usain Bolt pushes against the starting block, exerting an average force of

1700N. The force that the block exerts on his foot points 20 degrees above the horizontal. Determine his horizontal speed after the force is exerted for 0.32 seconds.

Mathematics

1 answer:

Leviafan [203] · Answer 1 · 2022-02-26T10:22:23+03:00

1) Determine the horizontal force, Fx, exerted by the block on Usain

cos(20°) = Fx / F => Fx = F*cos(20) = 1700N*cos(20) = 1597.48 N

2) Determine the Impulse of that force on Usain.

I = F*t = 1597.48N * 0.32s = 511.19 N*s

3) Determine change in momentum of Usain, Δp

Δp = I = 511.19 N*s

4) Find change if velocity

Δp = Δ(mV) = mΔV => ΔV = Δp / m = 511.19 N*s / 86 kg = 5.94 m/s

Given the Usain started from rest, the velocity is ΔV - 0 = 5.94 m/s

Answer: 5.94 m/s