I have not taken physics in over 10 years and I'm stuck on the following problem.

A boat goes $4 \frac{km}{hr}$ in still water, but there is current from east to west and you need your boat to go in a direction $15^{\circ}$ east of north. To do that you have to aim your boat $25^{\circ}$ east of north. What is the speed of the current?

I've tried setting it up by summing the velocity vectors of the boat and the current to get a resultant velocity vector for the final direction of the boat, $15^{\circ}$, but I'm getting to many unknown in my equation. Can someone help?


1 Answer 1


Consider two vectors, one has the direction $25^\circ$ east of north, with length 4 km/h (the boat speed and direction) and the other vector has direction east to west with unknown length. What we do know is that if you add up these two vectors by placing the start of one vector at the end of the other one, than the line that connects the start of the first one with the end of the second one, will point $15^\circ$ east of north.

If you draw this out you will get a triangle with angles 10, 65 and 105 degrees and one side of length 4. So you can compute the length of the east west line.


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