You work for the National Park Service testing a small cannon used to prevent av

Question

You work for the National Park Service testing a small cannon used to prevent avalanches by shooting down snow overhanging the sides of mountains. In order to detrmine the range of the cannon, it is necessary to know the speed with which the projectile leaves the cannon (muzzle speed), relatively to the ground. The cannon you are testing has a weight of Wc=500 lbs and shoots a projectile of weight Wp=20 lbs. During lab tests where the cannon is held and cannot move, the muzzle speed is v=415 m/s . You want to calculate the projectile's muzzle speed with respect to the ground under field conditions when the cannon is mounted so that it is free to move (recoil) when fired. You take the case where the cannon is fired horizontally using the same shells as in the laboratory.

The answer is not -16.598 or any variant of that number.

Explanation / Answer

by momentum conservation

Mcu =Mp(v-u)

u =Mpv/(Mp +Mc ) =20*415/520 =15.96

muzzle speed with respect to the ground =v-u =415-15.96 =399.04 m/s

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