Aboat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s. what is the velocity of the boat with respect to earth?

Explanation:

A boat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s.

Let north be positive y axis and east be positive x axis.

We have

         Velocity of boat = 4.5 j m/s

          Velocity of river = 3 i m/s

Velocity of the boat with respect to Earth = 3 i + 4.5 j

That is 56.31° north of east.

Velocity of the boat with respect to Earth is 5 m/s 56.31° north of east