Question

A vertical spring with a spring constant of 900 n/m has been compressed 0.8 m. The vertical spring is then used to launch a 2kg ball straight up into the air. How fast does it leave the spring gun? How high will the ball go?

Answer 1

Applying conservation of energy, find the speed:

$$E_P=E_K, \\\space\\ \frac12 kx^2=\frac12 mv^2,\\\space\\ v=x\sqrt{k/m}=17\text{ m/s}.$$

The maximum height:

$$h=\frac{v^2}{2g}=14.7\text{ m}.$$