I need help with a physics problem

Question

In a popular new mini hockey game, players use small launchers with springs to move a 5 gram puck. Each spring has a spring constant of 150 N/m and can be compressed up to 5 cm.

1. Solve for the maximum speed with which the puck can be launched. Show all of the work necessary to reach your solution. Start with general equations and explain what you are doing and why you did what you did.
2. Evaluate your solution. Describe how you evaluated your answer and whether or not you think your answer is reasonable.

Answer 1

This is a problem of energy where potential energy is equal to the kinetic energy when you drop a ball. The potential energy of the spring PE = 1/ 2 kx², and the kinetic energy of the puck KE= 1/2mv², equating

PE = KE, 1/2 kx² = 1/2 mv² , kx² = mv², v² = kx²/ m = 150 N/m ( 0.05m)² / 0.005 kg = 75 m²/s², v = 8.66 m/s

Answer 2

The general equations to be used are PE = 1/2 k X² and KE = 1/2 m V² where X is the displacement and V is the maximum velocity.

When friction is neglected, the maximum kinetic energy is equal to the potential energy when the spring is compressed to 5 cm (0.05 m). As the spring k is given in N/m, the displacement and mass should be in meters and kilograms.

1/2 x 0.005 kg x V² = 1/2 x 150 N/m x 0.05²m². Solving for V yields 8.66 m/s as the maximum velocity.

Keep in mind that at any given time the total mechanical energy is the sum of the potential energy and kinetic energy and as one increases the other decreases, but the sum is always constant.