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A boat moves relative to water with a ve...

A boat moves relative to water with a velocity v and river is flowing with 2v. At what angle the boat shall move with the stream to have minimum drift?

A

`30^(@)`

B

`60^(@)`

C

`90^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

(D) Let boat move at angle `theta` to the normal as shown in figure then time to cross the river `=1/(vcostheta)`
drift `x=(2v-vsintheta)(1/(vcostheta))` for x to be minimum
`(dx)/(d theta)=0=1(2sec theta tan theta-sec^2theta)` or `sin theta=1//2` or `theta=30^(@)` and `phi=90+30=120^(@)`
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