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March 26, 2017

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A shark, looking for dinner, is swimming parallel to a straight beach and is 90 meters offshore. The shark is swimming at a constant speed of 30 meter per second. At time t = 0, the shark is directly opposite a lifeguard station. How fast is the shark moving away from the lifeguard station when the distance between them is 150 meters?

  • calculus - ,

    make a diagram, you will have a right-angled triangle
    let the horizontal distance covered by the shark since t=0 be x m , and
    let the distance between the shark and the lifeguard be y m
    x^ + 90^2 = y^2
    2x(dx/dt) + 0 = 2y(dy/dt)

    when y = 150
    x^2 + 90^2 = 150^2
    x = √14400 = 120

    dy/dt = 2x(dx/dt)/(2y)
    = 2(120)(30)/300
    = 24 m/sec

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