A displacement boat (generally a moving object held up by buoyancyof the water) generates a wave that travels alongside at the speedof the boat with the first wave crest at the bow of the boat.Because the wavelength increases with the boat's speed, above acertain speed the second crest appears astern of the boat, so thatthe boat must travel uphill on the wave it creates. If it lacks thepower to get over the top of this wave, its speed is limited toroughly the speed of a wave with the length of the boat. Hence wehave the following rule of thumb:
The maximum speed of a modestly powered boat isapproximately equal to (actually, a little faster than) the wavewhose wavelength equals the length of the boat measured at thewaterline.

Empirically, the propagation velocity of water waves is

,

where is the wavenumber and is the gravitational constant. In parts that ask for numericalanswers, use .

a) Find the velocity of water wavesin terms of the wavelength .
An eight-person shell (or "eight") is alight rowing craft approximately 17.6-m long with eight rowers anda coxswain who steers and calls the stroke. Assume that the speedof the shell is limited according to the rule given in theintroduction.
b) Estimate the time it takes an "eight" to travel 2000 m.
c) Estimate the time it takes a good human swimmer, 1.80-m tall, to swim100 m. Assume that the speed of the swimmer is limited by his orher height.
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