Tennis ball $A$ is released from rest $50$ meters above the ground. Tennis ball $B$ is thrown upwards with an initial speed

of $15$ meters per second from a height of $5$ meters above the ground. Tennis ball $B$ is directly below tennis ball A and

tennis ball $A$ is dropped at the exact moment that tennis ball $B$ is thrown upwards.

a$)$ How long will it take for the tennis balls to collide?

b$)$ What is the velocity of each tennis right before the collision? In particular, which way is tennis ball $B$ moving?

c$)$ When they collide, what is their height above the ground and how far did each tennis ball travel?

d$)$ Now suppose the initial speed of tennis ball $B$ is unknown $($but everything else is the same$).$ Suppose tennis balls $A$

and $B$ collide when $B$ is at its maximum height above the ground. What was the initial speed of tennis ball $B?$

e$)$ Let's again suppose the initial speed of tennis ball $B$ is unknown $($but everything else is the same$).$ What is the

maximum initial speed of tennis ball $B$ such that tennis ball $B$ reaches the ground before it comes into contact with tennis

ball $A?$

SOLVE PART E