A \"pumpkin chucker\" designed for the annual pumpkin competition held near Mill

Question

A "pumpkin chucker" designed for the annual pumpkin competition held near Millsboro, delaware every fall (first week of November) uses a pneumatic launcher (air cannon) to throw its pumpkin. It is important to know if your "ammunition", the pumpkin, can withstand the force exerted on it during launch )otherwise it comes onto a solid wood board placed on the deck of their truck. The problem is that if the pumpkin bounces 1ft off the board after dropping from 5ft up, without obvious damage, the pumpkin is resilient enough to be used as ammo. What is the coefficient of restitution needed for good ammo.

Explanation / Answer

For a pumpkin which bounces from the ground with velocity u, rises to height h where it comes to rest (v=0)

By newton's tird eqn of motion

v^2 - u^2 = 2gh

v = 0

u is proportional to sqrt(h)

So coefficient of restitution = sqrt(1ft / 5ft)

= 0.447

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