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Calculus

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An object is dropped from the observation deck of the Skylon Tower in Niagara Falls, Ontario. The distance, in metres, from the deck at t seconds is given by d(t)=4.9t^2

a) the height of the observation deck is 146.9 m. How fast is the object moving when it hits the ground?

The answer is 53.655 m/s.

Could someone explain how the book got 53.655 m/s.

  • Calculus -

    First you find the time it takes to hit the ground ...
    4.9t^2 = 146.9
    t^2 = 29.98 sec
    t = √29.98 = 5.475

    if d(t) = 4.9t^2
    v(t) = 9.8t

    v(5.475) = 9.8(5.475) = 53.659 m/s

    Since you are in calculus, I am suprised that you did not know that the derivative of distance gives you velocity.

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