## College Physics (4th Edition)

The same gun will shoot the rubber ball up to a height of $4h$
When the spring is compressed a distance $x$, we can find an expression for the height $h$. By conservation of energy, the gravitational potential energy at maximum height will be equal to the elastic potential energy stored in the spring: $mgh = \frac{1}{2}kx^2$ $h = \frac{kx^2}{2mg}$ We can find an expression for the maximum height $h_2$ when the spring is compressed a distance of $2x$: $mgh_2 = \frac{1}{2}k(2x)^2$ $h_2 = \frac{k(2x)^2}{2mg}$ $h_2 = 4\times \frac{kx^2}{2mg}$ $h_2 = 4h$ The same gun will shoot the rubber ball up to a height of $4h$.