A powerboat heads due northwest at 11 m/s relative to the water across a river that flows due north at 5.4 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore?

Question

Henry · Answer

Vb = 11m/s @ 135o + 5.4m/s @ 90o.

X=11*cos135+5.4*cos90=-7.78 + 0=-7.78m/s
Y=11*sin135+5.4*sin90 =7.78+5.4=13.18 m/s.

tanAr = Y/X = 13.18/-7.78 = 1.69385.
Ar = -59.4o = Reference angle.
A = --59.4 + 180 = 120.6o = Direction.

Vb = X/cosA = -7.78/cos120.6=15.28 m/s=
Velocity of boat.