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Math Help - Optimisation QUS, need help plz

  1. #1
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    Optimisation QUS, need help plz

    Hello. I am having troubles working out this qus. Could you please show me, thanks ^^

    1) A motorbike is 30 km directly west of a car and begins moving east at 90km/h. At the same instant, the car begins moving north 60km/h. What will be the minimum distance between the vehicles?
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  2. #2
    Eater of Worlds
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    Let the car be at the origin. The bike is wwest of the car and heading east, so it's didtance at time t is 30-90t km. The car is heading north at 60, so it's distance at time t is 60t.

    The distance between them is ol' Pythagoras:

    (30-90t)^{2}+(60t)^{2}=D^{2}
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