Question

Miguel is driving his motor boat across the river. The speed of the boat in Still water is 14 mi/h. The river flows directly south at 2 mi/h. If Miguel heads directly west, what are the boats resultant speed and direction? Diagram is not drawn to scale.

Answer 1

Refer to the diagram shown below.

The resultant speed of the boar is v, and its direction is θ degrees south of west.

Use the Pythagorean Theorem to calculate v.
v² = 14² + 2² = 200
v = √(200) = 14.1 mi/h

By definition,
tan θ = 2/14 = 0.1429
θ = tan⁻¹ 0.1429 = 8°

Answer: 14.1 mi/h; 8° south of west.