Baseball Problem: Does a Ball Hit the Roof? Answer Here!

[jfeelz33]

Homework Statement

This is part of a calculus test and I am clearly missing something because this should be an easy problem: A baseball pitcher is having fun with the fans. He can throw a ball vertically froma point 6 feet above the ground at 75 miles per hour (110 ft/sec). He is standing in a domed stadium with a roof 200 feet above the ground. Does the ball hit the roof? Justify your answer.

We are currently doing integrals and just finished derivatives if that's any help. Any help would be appreciated, thanks.

The Attempt at a Solution

I sadly don't have one.

 

[Doc Al]

Clearly you need to figure out the maximum height the ball reaches. Can you write an expression for the height as a function of time?

You can start with the acceleration due to gravity and integrate if you like.