# Homework Help: Relative Velocity Boat Problem

1. Sep 20, 2015

### ECard

1. The problem statement, all variables and given/known data

You wish to paddle a boat across an 82 m wide river and land at a boathouse that is 14 m downstream of your starting point. If the current in the river is uniform at 0.50 m/s, how fast and in what direction do you need to row to reach the boathouse in 2.0 minutes?

2. Relevant equations
Relative Velocity equation
VBE = VBW + VWE

3. The attempt at a solution

I know that in 2 minutes I would end up 60 m downstream.
(120 s)(0.50 m/s) = 60 m

This is 60 - 14 = 46 m away from the boathouse

Which means that I would need to row upstream at
46 m / 120 s = .38333 m/s
And row across the water at a speed of
82 m / 120 s = .68333 m/s
to be able to reach my destination in 2 min.

From this I'm assuming that I can use Pythagorean equation to solve for the resultant vector.
sqrt[(46m/120s)2 + (82m/120s)2] = .78351061 m/s

And then the angle of direction through trig
theta = arctan( (82m/120s) / (46m/120s) ) = 60.7 degrees upstream and across

I'm not sure if this is right because from the equation I get that
VWE = 0.50 m/s

2. Sep 20, 2015