This year you have a summer job working for the National Park Service. Since the

Question

This year you have a summer job working for the National Park Service. Since they know that you have taken physics, they start you off in the laboratory which tests possible new equipment. Your first job is to test a small cannon. During the winter, small cannons are used to prevent avalanches in populated areas by shooting down heavy snow concentrations overhanging the sides of mountains. In order to determine the range of the cannon, it is necessary to know the velocity with which the projectile leaves the cannon (muzzle velocity). The cannon you are testing has a mass of 320 kg and shoots a 18-kg projectile. During the lab tests the cannon is held horizontally in a rigid support so that it cannot move. Under those conditions, you measure the magnitude of the muzzle velocity to be 400 m/s. When the cannon is actually used in the field, however, it is mounted so that it is free to move (recoil) when it is fired. Your boss asks you to calculate the projectile's speed leaving the cannon under field conditions, when it is allowed to recoil. She tells you to take the case where the cannon is fired horizontally using cannon shells which are identical to those used in the laboratory test.

Explanation / Answer

use the conservation of momentum
Initially everything is at rest. SO initial momentum is 0
So, final momentum must also be 0

m(cannon)*V(cannon) + m(projectile)* V(projectile) = 0
320*V + 18*400 = 0
V = -22.5 m/s
Negative sign implies the direction is opposite of muzzle velocity

Answer: 22.5 m/s

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