Please help! I'm not sure what equation or the process to do this question.

A 120 N/m spring is compressed 0.25m and is used to launch a 0.5kg ball. What is the momentum of the ball immediately after is fired?

The momentum is 1.94 kg m/s.

Explanation:

To solve this problem we equate the potential energy of the spring with the kinetic energy of the ball.

The potential energy of the compressed spring is given by

,

where is the length of compression and is the spring constant.

And the kinetic energy of the ball is

When the spring is released all of the potential energy of the spring goes into the kinetic energy of the ball; therefore,

solving for we get:

And since momentum of the ball is ,

Putting in numbers we get: