This otter can swim through the water. He swims at what he perceives as perpendi

Question

This otter can swim through the water. He swims at what he perceives as perpendicular across a wide stream.

She swims at across a wide river that flows at a much slower rate. But she swims in a direction that takes her directly across the river, on a path perpendicular to the shore.

You watch two otters cross a river of width d with water flowing at vw. Each otter swims at vo relative to the water and they take the paths described above. How much longer does the otter following the first otter take? To answer this, derive an expression for the ratio of the time taken by the otter following the second scenario to cross the river divided by the time taken by the otter following the first scenario to cross the river. Get the ratio in terms of vo and vw and explain

Explanation / Answer

Time taken by first otter t1 = d / vo

In second case, otter swims at angle theta relative to water,so vo sin theta balances river water velocity, vo cos theta is velocity perpendiculr.

time taken by second otter = d/[vo cos theta] and vo sin theta = vw, cos theta = sqrt(vo^2-vw^2)/vo

t2 = d/sqrt(vo^2-vw^2)

t2/t1 = vo/sqrt(vo^2 - vw^2)

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