You are in a boat that is traveling across a river from east to west at 4.0 m/s. the river runs north at 3.0 m/s. what is the resultant velocity of the boat?

Answer 1

Vb = 4m/s @ 180o + 3m/s @ 90o.

X = 4*cos180 + 3*cos90 = -4 m/s.
Y = 4*sin180 + 3*sin90 = 3 m/2.

tanAr = Y/X = 3/-4 = -0.7500
Ar = 36.87o = Reference angle.
A = 180 - 36.87 = 143o.

Vb = X/cosA = -4/cos143 = 5 m/s.