Slingshot

If a projectile is fired at an angle of 45 ° to the horizontal then the initial speed of the projectile and the distance it travels is related by $d = \frac{v^2}{g}$.

Use the conservation of energy in order to find the speed of the stone. The energy stored in a strip which is extended by $\delta x$ is equal $E = \frac{k \delta x^2}{2}$.