Ceiling height for a game of Catch

[Lukeblackhill]

Dear Mates,

I was studying Newton's Laws of Motion by Berkeley's Physics Course, Vol. 1 - Chap. 3, when I came across this problem, about finding the maximum separation of the boys. In my mind, it was simply about finding the "2x", considering x to be the distance between the first boy and the position of the ball at maximum height. Working with the equations of motion for a uniform gravitational field, the task would be resumed in applying the problem's variables to the equation R = Vo²sin2θ/g. But I don't know if this interpretation of mine is wrong of if I've made mistakes in the arithmetics, but I simply can't arrive in the result presented by the own book. And without knowing what I did wrong, I'm unable to give the explanation next requested.

Ceiling height for a game of catch. Two boys "play catch" with a ball in a long hallway. The ceiling height is H, and the ball is thrown and caught at shoulder height, which we call h for each boy, If the boys are capable of throwing the ball with velocity vo, at what maximum separation can they play?

Ans. R = 4V(H - h)[vo²/2g - (H - h)]. Show that if H - h > vo²/4g, R = vo²/g. Explain the physical significance of the condition H - h > vo²/4g.


Thank you for your help,
Cheers,
Luke

 

[kuruman]

The range equation that you have is correct as a starting point because the ball returns to the same height from which it was launched. What do you think you should do next? Show us what you have so far.

 

[J Hann]

The range formula is fine as a check, but you do not need to use trig
functions to get the answer provided for (R)^1/2.

 

[barnikbhaumik]

We know that the height attained by the ball is (v0²sin²ø)/2g<=H-h where H = the highest height attained and h is the height at which the ball is caught by the boys.
Sin ø=√{(H-h)*2g/V0²}
R= V0²/g*[2√{(H-h)*2g/v0²}][√{1-(H-h)*2g/V0²}]...simply to get the result

 

[haruspex]

applying the problem's variables to the equation R = Vo²sin2θ/g.

But that leaves you with the unknown angle. You need to find the best angle, given that you are not allowed to hit the roof.

 

[kuruman]

This is a revived thread from 2 years ago by new user. OP seems to have vanished.

 

[haruspex]

This is a revived thread from 2 years ago by new user. OP seems to have vanished.

Ah, thanks.