Juggling/Projectile Motion problem

[qswdefrg]

Homework Statement

A juggler can transfer a ball from his left hand to his right hand in 0.2s. If he is juggling 5 balls and releases them from a height of 1.5m what is the min. height of the ceiling?

Homework Equations

symmetrical trajectory equations:
t = 2v1sintheta / g
delta_d = v1_y^2sin^2theta / 2g

The Attempt at a Solution

I am assuming that the ball follows a parabolic shape and that the juggler's hands are 90 degrees. I am also setting their hands to be the zero position.

I'm stuck on how to find the time of one ball in the air. Since the juggler always has 1 ball in either hand, that means 3 balls in the air... so 3 x 0.2 = 0.6? But when I sub it into the equations, d = 0.44 m. That can't be right. The only answer that seems reasonable is 0.2 x 5 = 1s, resulting in displacement of 1.5m.

So ceiling has to be 1.5 + 1.2 = 2.7 m? This is pretty low.

 

[Redbelly98]

This is a tricky one just to think about and set up. Here are my thoughts:

1. Based on the 0.2s transfer time between hands, how many balls per second can the juggler handle?

2. Based on the answer to (1), what is the time for 1 ball to complete a cycle if there are (a) 5 balls, (b) 10 balls, and (c) 15 balls?

A "cycle" is one time completely around the ball's path, say from the right hand, upward through the air and back down to the left hand, then transferred from the left to the right hand.

Hope that helps.