Problem No$.4$: In a dart gun as shown below, a spring with Hooke's constant $k=100\frac{N}{m}$ is compressed $8$ cm when the dart $($mass $m=10$ gram$)$ is loaded.

$($a$)$ What is the elastic potential energy of the dart in the initial position?

$($b$)$ What is the velocity of the dart when the spring is released?

$($c$)$ What is the kinetic energy of the dart? $[$Hint: conservation of energy$]$

$($a$)$

$($b$)$