A river of width `w` is flowing such that the stream velocity varies with `y` as `v_(R)=v_(0)[1+(sqrt3-1)/wy]`, where `y` is the perpendicular distance from one bank.A boat starts rowing from the bank with constant velocity `v=2v_(0)` in such a way that it always moves along a straight line perpendicular to the banks.
What will be the velocity of the boat along the straight line when he reaches the other bank

Options

A. `v_(0)`
B. `sqrt2v_(0)`
C. `v_(0)/sqrt2`
D. `2c_(0)`

Answer

A

Explanation

When the boatman reaches the oppostie bank
`y=w` or `v_(R)=sqrtv_(0) or v cos alpha=V_(R)`
Hence, `(2v_(0))cos alpha =sqrt3v_(0)`
Hence resultant velocity will be
`v=v sin alpha=(2v_(0)) sin 30^(@),v_(y)=v_(0)`.