Question

A 14 kg cannon ball is fired from a 622 kg brass cannon on a frictionless, horizontal surface at an angle of 15º with respect to the horizontal. The cannon is constrained to move only in the horizontal direction. The initial velocity of the cannon ball is vi = 32 m/s. 1) Previous to launch, what is the net momentum of the ball and cannon system?

Answer 1

The net momentum of the system is zero.

Solution:

As per the question:

Mass of cannon ball, M = 14 kg

Mass of the cannon, m = 622 kg

Angle of inclination,
`\theta = 15^(\circ)`

Initial velocity of the cannon,
`v_(i) = 32 m/s`

Now,

In order to find the net momentum of the cannon and cannon ball system before the launch, we apply the principle of conservation of momentum to system:

`P_(in, cannon) + P_(in, ball) = P_(final, cannon) + P_(final, ball)`

Initially, the momentum of the system is zero.

Also, the velocity of the cannon ball in the horizontal direction equals the velocity of the brass cannon:

`v_(cannon) = v_(in, ball)cos\theta`

`v_(cannon) = 32cos15 = 30.91 m/s`