When the wind blows
A cyclist cycled a mile in 4 minutes against the wind. He returned in 3 minutes. How long would it have taken if there was no wind?
Labels: funphysics
posted by Chris at
7:27 PM
Sunday, January 17, 2010
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9 Comments:
Cam won't bother with this one(too easy for him)let's see what others say
Knighmare. He's done quite a few that are trivial (for him). Also he's merely excellent, not infallible, as you might see when he answers. I guess there's a 25% probability that he'll get this one wrong.
I've reconsidered. I doubt that Cam will get it wrong. I mis-guessed because of the way that the official answer is worded. Cam will reason more clearly than in the official solution.
In case anyone really thinks about the physics: you can assume that the rolling resistance is independant of speed. In fact it may be neglected entirely.
Although you might have been waiting for cam to post,
i found the answer to be about 3.43 minutes no wind
after losts of scribbling, I got
3 1/2 minutes each way for a total of 7 miinutes ... if I'm right, the winf had no effect on the overall time.
typo -> losts = lots in previous post
must be tired
winf = wind
I'll accept 3.43, that's actually half the time. 6 6/7 = 6.857... minutes is the answer sought. Well done Jayson.
I'll spare everyone the full physics, but it doesn't matter how the wind force depends on speed. Rolling resistance is probably neglible but doesn't affect the result if it is independent of speed (and that is approximately true).
The cyclists speed with the wind is v + w and against the wind is v - w, where v is the cyclist's air speed and w is the wind speed.
distance = speed * time.
1 = 3(v + w) = 4(v - w).
a) 3v + 3w = 1 and b) 4v - 4w = 1
4*a)+3*b) => 24v = 7 => v = 7/24 miles/min.
(The wind speed is 1/24 miles/min).
So he can do the 2 miles in 2/(7/24) = 48/7 = 6 6/7 minutes.
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