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At noon, ship A is 100km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 15km/h. How fast is the distance between the ships changing at 4:00pm?

  • Calc -

    At a time of t hrs,
    let the position of ship A be P and let the position of ship B be Q
    Join PQ, and complete the large righ-angled triangle
    having a base of 100 and a height of 15t + 30t or 45t
    (the horizontal distance between them is always 100 km
    PQ^2 = 100^2 + (45t)^2

    2 PQ d(PQ)/dt = 0 + 2(45t)(45)
    d(PQ)/dt = 2025t/D

    at 4:00 , t = 4
    PQ = √(100^2 + 180^2) = appr 205.913

    d(PQ)/dt = 2025(4)/205.913
    = 39.34 km/h

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