The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 $\mathrm{m}$ and the the gun fired vertically as shown, the gurcan launch a 20.0 -g projectile from rest to a maximum height of 20.0 $\mathrm{m}$ above the starting point of the projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring $(\text { where } x=0),$ as shown in Figure P5. 39 $\mathrm{b}$ .