$(15$ pts $)$ At a given instant, the football player A throws a football $C$ with a velocity of $24\frac{m}{s}$ in the direction shown when player $B$ is $15$ m away.

a$.$ Determine the distance from player A where player $B$ will catch the ball at the same elevation as it was thrown.

b$.$ Determine the maximum height from the point of the throw.

c$.$ Determine the constant velocity that player $B$ must run in order to catch the ball as stated in part a$.$

d$.$ Determine the magnitude of the ball's velocity at $10$ m $.$

e$.$ Determine the time after the throw when player $B$ catches the ball.