Question

A vertical spring gun is used to launch balls into the air. If the spring is compressed by 4.9 cm, the ball of mass 5.5 g is launched to a maximum height 50.2 cm. How much should the spring be compressed to send the ball twice as high?

Answer 1

We know, by conservation of energy :

`(kx^2)/(2)=mgh`

Therefore,

`(x_1^2)/(x_2^2)=(h_1)/(h_2)`

Putting given values, we get :

`(x_1^2)/(x_2^2)=(h_1)/(h_2)\\\\(4.9^2)/(x_2^2)=(50.2)/(2* 50.2)\\\\x_2^2=2* 4.9^2\\\\x_2 = 4.9* √(2)\\\\x_2=6.93\ cm`

Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.

Hence, this is the required solution.