The only thing I know about the Freeze is that no one can beat the Freeze (except with a generous head start). And he's awesome. In case you haven't seen, the Freeze is this guy in a turquoise spandex suit that challenges mere mortals to a race in the outfield of the Atlanta Braves SunTrust Park between innings.
Overall, this seems like a great physics problem. It's a variation of "a train leaves from Chicago traveling at 20 mph while a train leaves from New York traveling at 40 mph—where do they meet?" OK, it's a little bit different. But the physics is the same.
If I want a physics problem, the first thing I am going to need is data. I want the position of both "the Dude" and the Freeze. Since they aren't really running in a straight line, it's not super trivial to get their position as a function of time. Instead, I am going to pick certain identifiable points along their path and record their times at those points. I can estimate the distance between points on the field using the dimensions of SunTrust Park.
The second part is to look at the video of the Freeze and the Dude to record the time that they pass these marks. Of course I will use Tracker Video Analysis—even though I'm just marking a few points this software makes it easy to keep track of the times (instead of counting video frames).
But after that, I get the following plot for the motion of the two runners.
Here you can see that both the Freeze and the Dude seem to run at a fairly constant speed (I'm partially surprised). By fitting a linear function to each set of data, I can get the speeds for both runners. It seems the Freeze is going at around 8.24 m/s and the Dude is at 6.24 m/s. Both of those are fairly fast—I don't think they pick out average people to race the Freeze. You can also see that the Freeze gives the dude an almost 5 second head start (although the whole race was only about 25 seconds long) with the two runners meeting with only 3 seconds left.
Since there are too many unanswered questions, I am just going to use this data for the following homework questions. Yes, you have to answer them all. For all of these questions, assume the Freeze can run with a speed of 8.24 m/s.
- Suppose there was a runner with an average speed of 5 m/s. How long should the Freeze wait before starting his run so that he finishes the race at exactly the same time as the other person?
- A runner has an average speed of 6 m/s and the Freeze waits 3.5 seconds before starting his race. When and where does he catch up to the other person?
- Imagine the the Freeze runs with a constant acceleration of 0.5 m/s2. If the other runner travels at a constant speed of 7 m/s (and they both start at the same time), where do they meet? Or maybe the other person wins?
- I have this feeling that the Freeze uses a trick (in real life). The idea here is to give the person enough of a head start so that it looks cool but the Freeze still wins. One way to do this would be to just always give a 5 second head start. A better way would be to measure the time it takes the other runner to travel the first 10 meters as a method to estimate the runner's speed. Come up with a formula that uses this time to calculate the head start the Freeze should give and still win the race by 2 seconds.