Question

David can row at 5 m/s in still water. He starts rowing from a point on the south bank of a river that is flowing due east at 3 m/s and steers the boat at 90° to the bank. He is also being blown by a wind from
the north-east at 4 m/s.
Express the velocity of the boat as a component vector.

Answer 1

He is moving East (x direction) at 3 - 4 cos 45 = 0.172
His moving North (y direction) at 5 - 4 sin 45 = 2.172
speed^2 = 0.172^2 + 2.172^2
solve for speed magnitude
tan (angle above x (East) axis) = 2.172 / 0.172