A speed boat travels with a speed of 6 m/s travels directly north to cross a river flowing west with a current traveling at a speed of 3 m/s. What is the resultant velocity of the boat?

6.7 m/s @ 116.6°

Explanation:

Use Pythagorean theorem to find the magnitude:

v² = vx² + vy²

v² = (-3 m/s) ² + (6 m/s) ²

v = √45 m/s

v ≈ 6.7 m/s

Use trigonometry to find the direction:

θ = atan (vy / vx)

θ = atan (6 m/s / - 3 m/s)

θ = atan (-2)

θ ≈ 116.6° from the + x axis, or 63.4° north of west.