$(14$ pts$)$ You load and fire a ballistic. The ball is caught by the cup

$($the cup is initially at rest$),$ and the pendulum swings up$,$

stopping at the maximum height. Assume the speed of the ball

and cup immediately after the collision is $0\mathrm{.}740($m$)/($s$).$ The mass

of the cup is $0\mathrm{.}290$ kg $,$ and the mass of the ball is $0\mathrm{.}0820$ kg $.$

$($c$)(3$ pts$)$ What was the energy stored in the spring just before you press the trigger to launch

the ball?

$($d$)(3$ pts$)$ How much kinetic energy was lost in the collision between the ball and the cup?

Assume the system is the ball and the cup. Consider the system just before and just after the

collision but before the pendulum swings up$.$