A spring-loaded toy dart gun is shot to a height h. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed twice as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring

The height reached by the dart in the second shot is (4 H).

Explanation:

It is given that, a spring-loaded toy dart gun is shot to a height h. In this case, all the potential energy stored in the spring is converted to potential gravitational energy at the maximum height.

........(1)

At the second shot, the spring is compressed twice as far before firing. x' = 2x

.........(2)

h is the height reached by the dart in the second shot.

Dividing equation (1) and (2) as:

h = 4H

So, the height reached by the dart in the second shot is (4 H). Hence, this is the required solution.