John and Mary are skating at an ice rink. John skates at a constant speed of 6.7 m/s, with respect to the ice surface, directly south. Mary skates at a constant speed of 11.5 m/s in a direction of 34° west of south, with respect to the ice. What are the magnitude and direction of Mary's velocity with respect to John due south?

Question

Henry · Answer

V = 11.5m/s[236o] - 6.7m/s[270o]
V = 11.5*Cos236 + 11.5*sin236 - (-6.7i) = -6.43 - 9.53i + 6.7i = -6.43 - 2.83i

Tan Ar = Y/X = -2.83/-6.43 = 0.44074
Ar = 23.8o = Reference angle.
A = 23.8 + 180 = 203.8o, CCW = 66.2o W.
of S. = Direction.

V = X/Cos2o3.8 = -6.43/-.915 = 7.03 m/s.
= Magnitude.