# Vector - Need explanation

## Homework Statement

A girl can row a boat at 3 m/s in still water. She wishes to cross a 165m wide river in which the current flows at 1.5 m/s. Find the direction in which the boat must be steered in order to cross the river:

a) by the shortest possible route

b) in the shortest possible time

## The Attempt at a Solution

The answer from my book says that for

a) In order to cross the river by the shortest possible path, the actual path must be at right angles to the banks, which is θ=cos-1 1.5/3 = 60º

b) in order to cross in shortest possible time, the boat must be steered at right angles to the bank, i.e θ=90º.

But i don't really understand. Can anyone elaborate more for me...?

Why in order to cross the river by the shortest possible path, the actual path must be at right angles to the banks?

and why in order to cross in shortest possible time, the boat must be steered at right angles to the bank?

HallsofIvy
First, geometrically, the shortest path across a river, represented by two parallel lines, is perpendicular to the banks. If you need more detail, any other straight line across the river would form the hypotenuse of a right triangle having the perpendicular route as a leg. And $c^2= a^2+b^2$ so the hypotenuse is always longer than either leg. And any curved path is longer than the straight line between the two endpoints.