The speed of the boat on still water is 100km/h. The water flows from the west at a speed of 45km/h. In which direction must the sailor steer the boat in order to fly due to north?

Question

*What I don't understand is 'which way(direction) is the boat travelling?'

Thanks in advance.

Answer 1

Draw the velocity vector v, pointing kind of northwest, with length 100. At its end, add a vector pointing eastward, of length 45.

You want to figure the angle of the velocity vector so that when you add the two, the east-west component is zero. That is, the resultant velocity is due north.

So, if the velocity's direction is θ° west of north, you need

sinθ = 45/100
θ = 26.7°

So, if the pilot steers the boat on a course of 333.3°, he will end up going due north after the water pushes the boat eastward.