A boat man could row his boat with a speed 10 m/sec. He wants to take his boat from P to a point Q just opposite on the other bank of the river flowing at a speed 4 m/sec. He should row his boat–

Options

A. At right angle to the stream
B. At an angle of `sin^(-1)(2/5)` with PQ up the stream
C. At an angle of `sin^(-1)(2/5)` with PQ down the stream
D. At an angle of `cos^(-1)(2/5)` with PQ down the stream

Answer

B

Explanation

`|V_(n) sin theta|=| overset rarr V_(r)|` `overset rarr V_(t)=` Velocity of river
`10 sin theta= 4` `overset rarr V_(B)=` Velocity of boat
`sin theta = (4)/(10)=(2)/(5)` `overset rarr V_(Br)=` Velocity of boat w.r.t. river.
`theta = sin^(-1)(2/5)`