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5 August, 00:54

A rocket is launched from atop a 99-foot cliff with an initial velocity of 122 ft/s.

a. Substitute the values into the vertical motion formula h = - 16t^2 + vt + c. Let h = 0.

b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.

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  1. 5 August, 01:07
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    When t=0, h=0. Therefore c = 0

    The velocity function is the derivative of the distance function, which is

    v (t) = - 32t + v

    When t=0, v=122

    Therefore, the distance function is

    h (t) = - 16t^2 + 122t

    When the rocket hits the ground, h = - 99 ft.

    Therefore

    -16t^2 + 122t = - 99

    16t^2 - 122t - 99 = 0

    Solve with the quadratic formula to obtain

    t = (1/32) [122 + / - (122^2 + 4*16*99) ^0.5] = 8.365 or - 0.74 s

    Reject negative time.

    Answer: t = 8.4 s (nearest tenth)
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