Maximize Your Football's Flight in a Sports Hall: Physics Problem Help

[physics131]

I only have really started physics and I need help with this problem for homework.Any help is much appreciated!

A football is kicked from the
floor in a 7.00 m high
sports hall with an initial speed of 20.0 m/s. What is the maximum horizontal
distance it can
fly without touching the ceiling until it strikes the
floor?

 

[HallsofIvy]

Have you drawn a a picture? Let \theta be the angle the initial velocity vector makes with the floor. Do you know how to find the horizontal and vertical components of velocity in terms of \theta? There is no acceleration horizontally, so horizontal velocity stays is constant. Do you know how to find the horizontal distance the ball will go in t seconds?

There is a downward acceleration, g= 9.81 meters per second per second. Do you know how to find the height of the ball after t seconds? You should have as quadratic equation for the height and that should be 0 when t= 0. Can you find the other value of t when the height is 0? (In other words, when the ball hits the ground, ending it flight.
That will depend on \theta.) The value of x for that t is the horizontal distance the ball flies- that will also depend on \theta.

You want to find the value of \theta that maxizes that distance with the restriction that the height of the ball is always less than 7 meters.