Two ships A&B leave port at same time the ship A is north-west 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

Question

2)At what time they will be 150km apart

Answer 1

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=Xb-Xa = -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.