Mr. Smith was driving through northern Maine witha couple of his Physics student
ID: 1794656 • Letter: M
Question
Mr. Smith was driving through northern Maine witha couple of his Physics students, and they passed by the wind farm in Mars Hill. "I wonder," one of them said, "how fast the tip of one of those turbine blades is going." "I wonder," the other one said, "how far we'd fly if we hung on to the blade until it was at its highest point, and then let go." "Let's figure it out!" Mr. Smith said. So we did a bit of research, and a bit of estimation. Here's what we found: *Based on doing the 1001-1002-1003 count that you resort to when you don't have a stop watch handy, we concluded that it took about 8 seconds for the turbine to do a complete revolution. *The height of the turbine tower is 262 feet. *The length of the turbine blade is 115 feet. So...how long would the students go flying if they let go at the blade's highest point? And how far would they go?Explanation / Answer
The total distance around at the tip of the blade is 2r, where r is the length of the blade.
So the tip of the blade travels 772 feet in 8 seconds, which gives it a speed of 96.5 ft/s (That's about 66 mph, which really surprised everyone; the blade motion looks so sedate from a distance!)
At the top of the cycle, the student is 262 + 115 = 377 feet off the ground, and since they let go at the moment when the blade is at its highest point, all 96.5 ft/s is horizontal.
How long does it take them to reach the ground? Use 32.2 ft/s2 as the acceleration, and we find that the trip to the ground takes about 4.8 seconds.
How far does the student travel horizontally in that time?
Therefore d = vt = 96.5(4.8) = 463.2 feet, or around a twelfth of a mile
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