MATH

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A frustrated office worker throws his laptop out of his business’s high-rise
office building. The height, h, in meters of the laptop above the ground at t
seconds can be modelled by 2 h(t) 125 5t .
Estimate the instantaneous rate at which the laptop hits the ground.

  • MATH -

    sorry the equation is h(t)=125=125-5t^2

  • MATH -

    h(t) = 125 - 5t^2
    Take the derivative to find the velocity:
    v(t) = dh(t)/dt = -10 t

    Now:
    Find the time when height is 0.
    Find the velocity at that time.

  • MATH -

    but when h is 0 t=0....

  • MATH -

    h = 125-5t^2 = 0
    -5t^2 + 125 = 0
    t^2 - 25 = 0
    (t+5)(t-5) = 0

    t = -5
    t = 5 s.

    V = g*t = 9.8 * 5 = 49 m/s.

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