A displacement boat (generally a moving object held up by buoyancy of the water)

Question

A displacement boat (generally a moving object held up by buoyancy of the water) generates a wave that travels alongside at the speed of the boat with the first wave crest at the bow of the boat. Because the wavelength increases with the boat's speed, above a certain speed the second crest appears astern of the boat, so that the boat must travel uphill on the wave it creates. If it lacks the power to get over the top of this wave, its speed is limited to roughly the speed of a wave with the length of the boat. Hence we have the following rule of thumb:

Empirically, the propagation velocity of water waves is

Question: Estimate the time T_100 it takes a good human swimmer, 1.80-m tall, to swim 100 m. Assume that the speed of the swimmer is limited by his or her height.

Explanation / Answer

The human can be taken to be the displacement boat. So the wavelength of the waves it creates is equal to his/her height.

SO wavelength created is (lambda=1.80 m)

thus, (k=rac{2pi}{lambda}=3.49 m^{-1})

Thus max speed = (v=sqrt{rac{g}{k}}=sqrt{rac{9.80}{3.49}}=1.68 m/s)

Thus time taken is (t=100/v = 100/1.68 = 59.5 s)

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