# 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?

Nov 22, 2016

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.

$\therefore$Potential Energy of ball$=$Compression Energy of Spring.

$\therefore \textcolor{red}{m g h = \frac{1}{2} k {x}^{2}}$ , 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, $\textcolor{b l u e}{\frac{420}{1000} \times 9.8 \times h = \frac{1}{2} \times 35 \times {\left(\frac{9}{6}\right)}^{2}} .$

$\therefore h = 9.5663$ metres $= 9.57$ metres. (answer).