Falling Football

Date: 11 Jan 1995 10:36:57 -0500
From: Merr
Subject: (none)

Would you answer the following question?

If I were to drop a football off the top of Mile High Stadium, how long 
would it take for the football to hit the ground?  The height of 
the stadium is 305 ft.

Date: 13 Jan 1995 02:18:13 -0500
From: Dr. Sydney
Subject: Re: your mail--mechanics problem

Hello there!

        We are glad you wrote to Dr. Math.  You asked a classic problem in
physics.  When I do problems like this here is how I like to think about
them.

        First consider all the parameters of the problem.  The only thing we
have working here in your problem is gravity, which is pulling the ball
toward the earth.  Let's call that quantity  g  (g is approximately 9.8
m/s^2).  So we have  a = g, where a is acceleration, right?

        Okay, now let's figure out the best approach to the problem.  We
want the TIME it takes for the ball to hit the ground.  We have an equation
for acceleration, so we can integrate twice to get an equation for distance,
right?  If we call the ground distance 0 and the top of the stadium 305 ft.,
then when the distance equation equals 0, the ball has hit the ground,
right?  So, all we need to do is find the distance equation, set it equal
to 0 and solve for t. 

        I'll help you with the first step, then maybe you can take it from
there, okay?  Let's integrate our equation for acceleration.

        Integral of a = v (where v is velocity)

So, we have:

        v = Integral of g = gt + c

        (where c is the initial velocity.  in this problem, the initial
velocity is 0, so c = 0)

So, you have:

        v = gt

Now, integrate again, and finish up the problem!  If anything is unclear or
confusing, or if you want to check your problem, feel free to write back.

--Sydney