# A ball with a mass of 80 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 6  kgs^-2 and was compressed by 4/5 m when the ball was released. How high will the ball go?

The spring potential energy in the spring, ${E}_{p \left(s\right)} = \frac{1}{2} k {x}^{2} = \frac{1}{2} \cdot 6 \cdot \frac{4}{5} = 2.4$ $J$, will all be converted into gravitational potential energy when the ball is at its highest point. ${E}_{p \left(g\right)} = m g h$. Rearranging, and expressing the mass in $k g$: $h = {E}_{p \left(g\right)} / \left(m g\right) = \frac{2.4}{0.080 \cdot 9.8} = 3.06$ $m$