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If a rock is dropped from a height of 66 ft, its poistion t seconds after it is dropped until it hits the ground is given by the function s(t)=−16t^2+66 .

Round values below to 3 decimal places.

How long does it take the rock to hit the ground?

_____seconds

Find the average velocity of the rock from when it is released until when it hits the ground.

______feet per second

What time after the rock is thrown will its instantaneous velocity be equal to its average velcity? (Apply the Mean Value Theorem)

___seconds after it is thrown

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3 answers

  1. really? They told you that its height after t seconds is
    h = −16t^2+66
    so, how long does it take to hit the ground? (height = 0)
    16t^2 = 66
    t^2 = 66/16
    t = 1/4 √66 ≈ 2.031 s

    you also know that speed = distance/time, so its average velocity is
    -66ft/(1/4 √66)s = -264/√66 ≈ -32.496 ft/s

    you know that since h = −16t^2+66, v = -32t
    so v = avg velocity when
    -32t = -264/√66
    t = 264/(32√66) ≈ 1.015 seconds
    Note that 1.015 < 2.031 as guaranteed by the MVT.

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  2. solve −16t^2+66 = 0
    use that to get avg velocity: -66/t
    find where -32t = avg velocity

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  3. Explain more?

    If I understood what this meant, I clearly would have the answer already.

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