A swimmer crosses a river, taking the least possible time by directing his strokes perpendicularly across. The river is 10m wide and flows at a speed of 4ms-1 and he swims at a speed of 2.5 ms-1, at what distance downstream would he arrive at the other bank? If he wanted to reach a point directly across from where he starts (i.e swimming shortest possible distance) at what angle to the bank and in which direction should he direct his strokes?
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Answer:
Explanation:
time of travel when starts perpendicular = 10/2.5 = 4 sec
drift = 8m
just want to reach opposite end
sin theta = 2.5/4
sin theta = 25/40
sin theta = 5/8
theta = arc sin 5/8
and he should head the target along upstream direction that means he should opposite of downstream and incbetween of bank perpendicular line line and upstream
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