A boat, propelled so as to travel with a speed of 0.50m/s in still water, moves directly across a river that is 60m wide. The river flows with a speed of 0.30m/s. (a) At what angle, relative to the straight across direction, must the boat be pointed? (b) How long does it take the boat to cross the river?
Answer: (a) 37 degrees upstream (b) 1.5x10^2 seconds.
The Attempt at a Solution
I tried to use the movement of the boat at 0.50m/s with the 60m across and found that that would take 120 seconds. Then, I multiplied the 120 seconds by the river current speed of 0.30m/s to find that it would pull the boat 36 meters downstream. Then I tried to find the angle using tan(theta) = opp/adj but I got the angle 31 degrees.
I tried several other methods last night that I can't remember now, and I kept getting 31 degrees. The book states that it is 37 degrees, however, and so I'm wondering what I'm doing wrong.