Awoman 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.