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ahmadu university zaria nigeria

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Ship A is sailing due south at 25 km/hr. At the same time, a second ship B, 50km miles south of A, is sailing due east at 20 km/hr.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant

  • calculus - ,

    Let B start at (0,0). Then the positions of the boats at time t are
    A(t) = (0,50-25t)
    B(t) = (20t,0)
    and the distance d is thus
    d^2 = (20t)^2 + (50-25t)^2
    = 1025t^2 - 2500t + 2500
    2d dd/dt = 2050t - 2500

    At t=1, d ~= 32
    64 dd/dt = 2050-2500
    dd/dt = -7.03 km/hr

    At t=2, d = 40
    80 dd/dt = 4100-2500
    dd/dt = +20

    dd/dt=0 when t=1.22 so d = 31.23

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