Question

A spring-loaded toy gun is used to shoot a ball straight up in the air. (Figure 1) The ball reaches a maximum height H, measured from the equilibrium position of the spring.The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to H.

Answer 1

If  the spring is compressed by x , the potential energy stored in it = (1/2)*k*x^2

the potential energy is converted to potential energy of the bal when it reaches maximum height.

(1/2)*k*x^2= mgH

If the spring is compressed only half as far before firing then potential energy=(1/2)*k*(x/2)^2= (1/4)*(1/2)*k*x^2

potential energy of the ball at its maximum height= (1/4)*mgH

now the ball goes H/4 distance