What is the resulant velocity of a boat traveling west at a speed of 24 m/s across a river that is flowing south at 9 m/s?

Answer 1

The magnitude of the vector r is (using the Pythagorean Theorem) √(24² + 9²) = √657 = 25.63 m/s (I'll let you round to whatever significant figures you wish).

The direction of the vector r is found by tan(θ) = 9/24 so θ = tan^-1(9/24) = 20.56° south of west

In Direction nomenclature that would be S69.44°W (90° - 20.56° = 69.44°)

In Bearing nomenclature that would be 249.44° (270° - 20.56° = 249.44°)