A $12\mathrm{.}96$ g bullet is fired into a $5\mathrm{.}000$ kg ballistic pendulum suspended by $2\mathrm{.}000$ m cords. When the bullet strikes the pendulum block it embeds into the block, making this an $($elastic$/$inelastic$)$ collision.

Upon impact the pendulum swings through an arc of $28\mathrm{.}84.$

a$)$ The pendulum increased it's height by m$,$ which corresponds to an increased gravitational potential energy of PEg $=$ J$.$

b$)$ This means the block$/$bullet combination had a total kinetic energy of KE $=$ J at the bottom of the arc, at the moment the bullet was brought to rest in the block, which corresponds to a velocity of V $=$ m$$s$-1,$ and a total momentum of P $=$ kg$$m$$s$-1,$ after the collision of the bullet with the pendulum block.

c$)$ Since the pendulum block had a total momentum of Pblock $=$ kg$$m$$s$-1$ before the collision, the bullet by itself had a momentum of Pbullet $=$ kg$$m$$s$-1$ before the collision, which corresponds to a velocity of Vbullet $=$ m$$s$-1,$ to $3$ significant digits only please.

d$)$ A second rifle is brought in and fired at the same pendulum block. This time a $19\mathrm{.}44$ g bullet, with a pre$-$collision velocity of Vbullet$-2=781$ m$$s$-1$ embeds into the block, causing it to swing through an arc of $.$