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.