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November 24th, 2012, 11:55 AM   #1
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Football angles

I was thinking about the problem of the running back and safety when the former has a clear path to the endzone and the latter is trying to run him down. Assume that the runningback is at point Pr the safety at Ps each with their own speeds (Vr and Vs) What is the yard-line that the safety can catch the running back and what paths should they be taking to have the best outcome for each of them ?

I thought there would be something like this online, but I could not find it.
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November 24th, 2012, 04:17 PM   #2
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Re: Football angles

I'm sure you can work this out with vectors and triangles, assuming that the runner continues to go in the same direction and speed ... in other words, his velocity vector is constant.

What's much more interesting in real life is that the runner will go in a particular direction at a particular speed; and as soon as the defender commits to that line of intersection; the runner "jukes" and radically changes his direction and/or speed so that he can't be caught. Sometimes the runner will even slow down then pick a new direction and get by the defender.

That seems like a more interesting situation to try to model. The key point is that the runner can make a change of velocity (direction and/or speed) a moment before the defender can react. That small interval when the runner knows where he's going but the defender doesn't, is what makes all the difference. If you vary the reaction time of the defender, you'll alter the zone in which the runner gets past the defender.

I'm sure the people who design fighter jets have given this a lot of thought. Another variant on this problem.
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November 24th, 2012, 05:46 PM   #3
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Re: Football angles

The runner's velocity vector is not constant. They seem to be aiming for the end of the goal line, however they're not running straight line but a curved one. The extra distance the running back has to do this way must be less than the extra distance the safety has to (he's coming from an angle), resulting in a tackle further down the field.
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