$$ A Completely inelastic collision is a collision where two objects stick together after collision. Both objects will have the same speed after collision: v$1$f $=$ v$2$f $=$ V$.(20$ points$)$

$($a$)$ A $7$ kg object moving to the right with a speed of $8$ ms$-1$ collides with a $3$ kg object moving to the left with a speed of $5$ ms$-1$ If the collision is completely inelastic.

$($i$)$ Calculate their speed after the collision.

$($ii$)$ Calculate the kinetic energy lost during the collision.

$$

$($b$)$ A bullet of mass $0\mathrm{.}05$ kg is fired into a pendulum of mass $10$ kg$.$ The bullet is embedded in the pendulum and the pendulum rises to a height of $2$ m$.$ Calculate the speed of the bullet.