calculus 1

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At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

  • calculus 1 -

    at t=5
    A west of origin 20+21*5 = 125 or x=-125
    B north of origin = 18*5 = 90 or y = 90
    h^2 = x^2+y^2
    h=(x^2+y^2)^.5 = 154 where h is hypotenuse

    we want dh/dt
    2 h dh/dt = 2 x dx/dt + 2 y dy/dt

    2(154) dh/dt = 2(-125)(-21) + 2 (90)(18)

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