Dyanamics

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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
2)At what time they will be 150km apart

  • Dyanamics -

    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.

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