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A man wishes to cross a river in a boat....

A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes `10 min` with a drift of `120 m`. If he crosses the river taking shortest route, he takes `12.5 min`. Find the velocity of the boat with respect to water.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Let `v_r`=velocity of river
`v_(br)` = velocity of river in still water and
`omega=width of river`
Given `t_(min)=10 min or omega/v_(br)=10….(i)`

Drift in this case with be,
`x=v_rt`
`:. 120=10v_r....(ii)`
Shortest path is taken when `v_b` is along AB. In this case,

`v_b=sqrt(v_(br)^2-v_r^2)`
Now, `12.5=omega/(v_b)=omega/(sqrt(v_(br)^2-v_r^2)).....(iii)`
Solving these three equations, we get
`v_(br)=20 m//min,`
`v_r=12m//min`
and `omega=200m`
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