How to Calculate Rowing Speed and Direction to Reach a Boathouse?

[ECard]

Homework Statement

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?

Homework Equations

Relative Velocity equation
V_BE = V_BW + V_WE

The Attempt at a Solution

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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
V_WE = 0.50 m/s

 

[mooncrater]

I think your answer is correct. But I don't understand your last line :
"I'm not sure if this is right because from the equation I get that
V_WE = 0.50 m/s"

And in your relative velocity equation , I don't get what does that "W" represent.