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 The maximum speed of a modestly powered boat is approximately equal to actually, a little faster than) the wave whose wavelength equals the length of the boat measured at the waterline.

Empirically, the propagation velocity of water is
v-√2/k
where k is the wavenumber and g is the gravitational constant. In parts that ask for numerical answers, use g=9.81m/s2?
estimate the time t100 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.

Answer 1

The estimated time it takes for a good human swimmer, who is 1.80 m tall, to swim 100 m is approximately 55.56 seconds, assuming their speed is limited by their height.

The time it takes for a swimmer to swim a certain distance can be estimated by dividing the distance by the swimmer's speed. In this case, the swimmer's speed is limited by their height.

To estimate the time it takes for the swimmer to swim 100 m, we need to consider the swimmer's height and the speed at which they can swim.

Given:

- Height of the swimmer: 1.80 m

The speed of the swimmer is limited by their height, which means they cannot swim faster than their own height in one second. Therefore, the swimmer's speed can be approximated as 1.80 m/s.

To find the time it takes to swim 100 m, we divide the distance by the speed:

Time (t100) = Distance / Speed

t100 = 100 m / 1.80 m/s

Using a calculator, we can calculate the time:

t100 ≈ 55.56 seconds

Therefore, it would take a good human swimmer, who is 1.80 m tall, approximately 55.56 seconds to swim 100 m.