Posted by vinod on .
Two ships A&B leave port at same time the ship A is northwest at 32km/hr & ship B is 40degree south of west at 24 m/hr determine 1)the speed of ship B relative to ship A
2)At what time they will be 150km apart

Dyanamics 
Henry,
1. A = 32km/h[135o],CCW
Xa = 32*cos135 = 22.63 km/h
Ya = 32*sin135 = 22.63 km/h
B = 24km/h[220o],CCW
Xb = 24*cos220 = 18.39 km/h
Yb = 24*sin220 = 15.43 km/h
Xa and Xb are in same direction. So we
subtract:
Xc=XbXa = 18.39  (22.63)=4.24 km/h
Yc = Yb+Ya = 15.43 + 22.63 = 7.2 km/h
tanC = Yc/Xc = 7.2/4.24 = 1.69811
C = 59.5o
Vb=Yc/sinC = 7.2/sin59.5=8.36 km/h[59.5]
= Velocity of B relative to A.