A student can swim with a speed V in still water. She swims across a river of wi

Question

A student can swim with a speed V in still water. She
swims across a river of width W and back. The river
has a current of speed U, as shown in the figure. She swims in a path so that she travels directly
from one side of the river to the other, such that her displacement is perpendicular to the
shoreline.
Instead of swimming in a path so that she travels directly from one side of the river to the
other, she wants to go across in the shortest time possible knowing that
she will end up downstream a bit. What is the shortest time for the swimmer to get across the
river and back? (Derive an expression in terms of U,W, V)

Explanation / Answer

let her swim at an angle to the shoreline upstream.

so, Vx = Vcos + U

Vy = Vsin

time taken to cross the river = W/Vsin

this time will be minimum when sin is maximum i.e =90

so minimum time to get across and come back = 2W/V

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