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. The boat crosses the river from A to the other side in shortest possible time, then how far is the boat from the port B after crossing the river

Options

A. `(D)/(sqrt2)`
B. `sqrt2D`
C. `2D`
D. `(D)/(2)`

Answer

D

Explanation

The trip takes time `t=(D)/(v)`. The y-component of the total velocity is u. So the boat is at a distance`u(D)/(v)=(D)/(2)` Downstream from the port B after crossing. Take positive x-axis along east and positive y-axis along north.