Chapter 2: Problem 26
A typical value for the coefficient of quadratic air resistance on a cyclist is around \(c=0.20\) \(\mathrm{N} /(\mathrm{m} / \mathrm{s})^{2} .\) Assuming that the total mass (cyclist plus cycle) is \(m=80 \mathrm{kg}\) and that at \(t=0\) the cyclist has an initial speed \(v_{\mathrm{o}}=20 \mathrm{m} / \mathrm{s}\) (about \(45 \mathrm{mi} / \mathrm{h}\) ) and starts to coast to a stop under the influence of air resistance, find the characteristic time \(\tau=m / c v_{\mathrm{o}} .\) How long will it take him to slow to \(15 \mathrm{m} / \mathrm{s} ?\) What about \(10 \mathrm{m} / \mathrm{s} ?\) And \(5 \mathrm{m} / \mathrm{s} ?\) (Below about \(5 \mathrm{m} / \mathrm{s}\), it is certainly not reasonable to ignore friction, so there is no point pursuing this calculation to lower speeds.)
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