Question

A ball with a mass of `420 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `35 (kg)/s^2` and was compressed by `9/6 m` when the ball was released. How high will the ball go?

Answer 1

The height gained by the ball is `9.57` metres approx.

Explanation:

When the ball is projected vertically, it acquires a new potential energy, while the spring acquires the compression energy because of it's compression.

`:.`Potential Energy of ball`=`Compression Energy of Spring.

`:.color(red)(mgh=1/2kx^2)` , where,

m is mass of ball,
g is acceleration due to gravity,
h is height gained by the ball,
k is spring constant,
x is compression of the spring.

So, `color(blue)(420/1000xx9.8xxh=1/2xx35xx(9/6)^2).`

`:.h=9.5663` metres `=9.57` metres. (answer).