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A river is following from west to east a...

A river is following from west to east at a speed of 5m/minute. A boy on the south bank of the river, capable of swimming at 10 meters/minute in still water, wants to swin across the river in the shortest time, (i) Find the direaction in which he should swin, (ii) find the direction when drift along the river is zero.

Text Solution

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Given that, ` V_(R) = 5` m/minute. Let the boy try to swim in a direction ` theta^(@)` , west of north velocity of boat with respect to rvier ` V_(b,R)=10` m/minute

` t= d/(V_(b.R) cos theta)`
when time is minimu, when ` V_(b,R) cos theta` is maximum then, ` cos theta = 1 Rightarrow theta = 0 ^(@)` swimmer is swin in the north direction i.e., directly across the river.
(ii) when horizontal drift, is zero, then velocity of swimmer w.r.t ground along x-axis is zero.
i.e, ` v_(R) - v_(R) -v_(b,R) sin theta =0`
` V_(b,R) sin theta = V_(R)`
`sin theta = V_(R)/V_(b.R) =5/10 = 1/2 sin 30^(@)`
` theta = 30^(@)`
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