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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
VBE = VBW + VWE
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
VWE = 0.50 m/s