Achild walks due east on the deck of a ship at 2 miles per hour. the ship is moving north at a speed of 18 miles per hour. find the speed and direction of the child relative to the surface of the water.

Refer to the figure shown below.

The velocity of the child and the velocity of the ship should be added vectorially to find the speed and direction of the child relative to the water surface.

The magnitude of the child's velocity is
v = √(2² + 18²) = 18.11 mph

The direction of the child's speed is
θ = tan⁻¹ (18/2) = tan⁻¹ 9 = 83.7° north of east or counterclockwise from the eastern direction.

The magnitude is 18.1 mph.
The direction is 84° north of east.