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Q & A: gravity and Galileo's superposition

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Most recent answer: 04/16/2011
Q:
How long would it take an object to fall from a fixed height to the ground? I am using this to calculate a question for my son who pole vaults. The front tip of his pole is about 14' off the ground while he is running. He has to plant this tip in the planting box, that is actually 8" down from the runway, to take off the ground. I want to know how long it takes the tip to drop via gravity so that by adding this info to his velocity of about 25.5 ft/sec, I can estimate where along his approach run he could let the tip fall and hit the ground/back of planting box as he is ready to take off the ground. Thanks in advance for your insight.
- Alan Abernethy (age 45)
Summerville, SC, USA
A:
The rotation of a pivoted uniform rod in a gravitational field is a standard problem in freshman mechanics courses. I can't give you a precise time, because I don't know quite how he holds the pole. What I can give is a useful technique.

To the extent that you can neglect air friction on the pole, the rate at which it rotates down is entirely independent of the sideways motion. That comes from the earliest versions of relativity, due to Galileo. So if your son stands still and lets the rod rotate, you can just time it with a stop watch. The same time should work when he's running.

Mike W.

(published on 04/16/2011)

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