Math Gr 11

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"A rock is dropped from the edge of a 180 m cliff. the function f(x) = -5t^2 - 5t + 180 gives the height of the rock, h(t), in meters t seconds after it was released. How long does it take for the rock to reach a ledge 80 m above the base of the cliff?"
I have no idea how to solve this, steps and explanations would be amazing.

  • Math Gr 11 -

    well, since f(t) is the height of the rock at time t, just set it to 80 and solve for t:

    -5t^2 - 5t + 180 = 80
    5t^2 + 5t - 100 = 0
    t^2 + t - 20 = 0
    (t+5)(t-4) = 20

    t=4

    check:
    f(4) = -5(16)-5(4)+180 = 80

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