Question

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?

Answer 1

6.7 m/s @ 116.6°

Step-by-step 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.