A boat moves relative to water with a velocity `v` which is `n` times less than the river flow velocity `u`. At what angle to the stream direction must the boat move to minimize drifting ?

Options

A. `theta=sin^(-1)(v/u)`from normal direction
B. `theta=cos^(-1)(v/u)`from normal direction
C. `theta=tan^(-1)(v/u)`from normal direction
D. `theta=sin^(-1)(u/v)`from normal direction

Answer

A

Explanation

In this problem, one think should be carefully meted that the velocity of boat is less than the river flow velocity.In such a case, boat cannot reach the point directly opposite to its starting point, i.e. drift can never be zero.Thus, to minimize the drift, boat starts at an angle `theta` from the normal direction up stream as shown Now , again if we find the components of velocity of boat along and perpendicular to the flow, these are, velocity along the river, `v_(x)=u-vsintheta`.
take taken to cross the river is `t=d/v_(y)=d/(v cos theta)` or `x=(ud)/v sec theta-d tan theta`
The drift `x` is minimum, when `(dx)/(d theta)=0`, or `((ud)/v)(sec theta. tan theta)- d sec^(2) theta=0`
or `u/v sin theta=1 or sintheta=v/u=1/n(as v=u/v)`