Problem Statement $2$:

A rotational catapult is designed to launch a $10-$pound projectile. The catapult consists of a rigid beam $($lever

arm$)$ pivoted at one end, with a length of $15$ feet. The other end of the beam has a spring$-$loaded mechanism

that, when released, imparts both linear and angular motion to the projectile. Consider that the spring

constant of the mechanism is $200lb\frac{m}{f}t$; compression distance of the spring before release is $0\mathrm{.}5$ feet; the

projectile is launched at $45$ above the horizontal and there is NO air resistance and massless beam.

Perform the following activities:

a$.$ Calculate the potential energy stored in the spring before release.

b$.$ Determine the angular velocity $()$ of the beam immediately after the spring is released.

c$.$ Compute the linear velocity $(v)$ of the projectile at the moment of release.

d$.$ Analyze the projectile's motion post$-$release to find:

b$)$ Time of flight $(T)$

c$)$ Maximum height reached $(H)$

d$)$ Horizontal range $($R$)$

e$)$ Evaluate the torque $(T)$ exerted by the spring on the beam during compression.

f$)$ Determine the moment of inertia $($I$)$ of the system.

Please include precidures Thanks!!