Two ports, A and B, on a north-south line ar separated by a river of width D. The river flows east with speed u. A boat crosses the river starting from port A. The speed of the boat relative to the river is v. Assume `v=2u`
Q. Suppose the boat wants to cross the river from A to the other side in the shortest possible time. Then what should be the direction of the velocity of boat relative to river?

Options

A. `30^@` west of north
B. `30^@` east of north
C. `60^@` west of north
D. along north

Answer

B

Explanation

To cross the river the fastest, we need to maximize the y-component of the total velocity is `V_(B)costheta` So `theta=0`. The boat should head straight to the north.
Take positive x-axis along east and positive y-axis along north.