Falling FootballDate: 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 |
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