Calculus III, how to do this vector problem.?

Question

A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 24 mi/h. Find the speed and direction of the woman relative to the surface of the water.

______mi/h (speed)

N _______°W (direction)

Answer 1

Draw a triangle looking from above, like the other guy said. There is a vector in the Northerly direction of 24mph and a vector in the westerly direction of 3mph.

So using vector addition (and Pythagoras' theorem) we find the resultant vector (the speed of the woman relative to the water) has a magnitude of 24.19 mph.

Using tan ratio the direction is N 7.13* W.

Answer 2

Think about it from above, and describe the velocities as vectors with respect to the water.

It becomes a simple right triangle.