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gfr · Mar 27, 2014, 09:22 AM

A man can row at 1m/s when his boat is in fixed, stationary water.
In a river, water flows at 0,5m/s.

If the man tries to cross the river in which direction (angle with respect to the line that crosses the river) he needs to direct his boat to get to the opposite side of the river?

My answer is arcsin (1/sqrt(5)) which is 29,56°

Is that right?

Thanks
Giovanni

ebaines · Mar 27, 2014, 10:13 AM

No, not right. Think about adding two vectors - one of magnitude 1 in an unknown diretion and the other of magnitude 0.5 parallel to the water flow, such that the resulting sum of the two vectors is perpendicular to the water flow.

gfr · Mar 27, 2014, 11:45 AM

Ebaines,
first of all thans.
That's exactly what I did.
If you want the resulting vector to be perpendicular to the water flow you need to add to the vector (0; -1/2) a vector which is (1; 1/2).
So you have 1/2 = 1/2*sqrt(5)*sin (x) and x = arcsin (1/sqrt(5)).

Do you agree ?
Ciao
Giovanni