A $0\mathrm{.}25-kg$ skeet $($clay target$)$ is fired at an angle of $28$ to the horizontal with a speed of $25\frac{m}{s}.$ When it reaches the maximum height, it is hit from below by a $15-g$ pellet traveling vertically upward at a speed of $230\frac{m}{s}.$ The pellet is embedded in the skeet.

a$)$ How much higher $(h^{\text{'}})$ does the skeet go up$?$

b$)$ How much extra distance $({}_x)$ does the skeet travel because of the collision?