# Boat crossing river problem using reference frames

1. Oct 2, 2011

### leroyjenkens

1. The problem statement, all variables and given/known data
A 110-m-wide river flows due east at a uniform speed of 3.3 m/s. A boat with a speed of 8.6 m/s relative to the water leaves the south bank pointed in a direction 37 degrees west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground? Give the direction as the angle of the velocity from due north, positive if to the east and negative if to the west. (c) How long does it take for the boat to cross the river?

2. Relevant equations
I was using the PA = PB + BA equation. Which is supposed to be set up like this: the velocity of something with respect to something else, equals, the velocity of something with respect to something else, plus, the velocity of something with respect to something else. Now I know how to do this problem, because it's simple enough to do without using the equation I just mentioned. But I was supposed to use this equation to do the problem.
What I did instead was I just thought about it logically. The river is moving east and the boat is moving in the westward direction, so I separated the boat's velocity into X and Y components and subtracted the X component from the velocity of the river and then solved from there.

But as far as the equation goes, how do I set up the equation? Which velocity goes on the left side of the equation and which velocities go on the right side? As far as I can tell, it makes a huge difference.
I tried using that equation to solve the problem, but the way I set up the equation, I ended up with an equation that would add the boat's velocity to the river's velocity, which would mean the boat would go faster in the west direction, even though the river is moving east. That would make no sense.
So anyone know how to set up that equation? In my book it's under the "Relative Motion in One direction" section, if that helps.

Thanks.