A woman walks due west on the deck of a ship at 3 miyh. The ship is moving north at a speed of 22 miyh. Find the speed and direction of the woman relative to the surface of the water.

v ≈ 22.2 mph

θ ≈ 7.8° west of north

Explanation:

vₓ = - 3 mph

vᵧ = 22 mph

Finding the speed (magnitude of velocity):

v = √ (vₓ² + vᵧ²)

v = √ ((-3) ² + (22) ²)

v ≈ 22.2 mph

Finding the direction

θ = atan (vᵧ / vₓ)

θ = atan (22 / - 3)

θ ≈ - 82.2° or 97.8°

θ is in the second quadrant, so θ ≈ 97.8°, or 7.8° west of north.