Pre-Calculus

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A pomegranate is thrown from a ground level straight up into the air at time t = 0 with velocity 67 feet per second. Its height at time t seconds is f(t)=-16^2+67t.

(a) Find the time it hits the ground and (b) the time it reaches its highest point. (c) What is the maximum height?
Please round to two decimal places.

  • Pre-Calculus -

    a) when it hits the ground, f(t) = 0
    0 = -16t^2 + 67t
    16t^2 - 67t = 0
    t(16t - 67) = 0
    t = 0 or t = 67/16 = appr 4.19 seconds
    t=0 would be the start of the toss

    so the answer you want is t = 4.19 sec

    b) since you labeled it "pre-calculus" I assume you cannot at this point take the derivative, too bad

    so we have to complete the square

    f(t) = -16t^2 + 67t
    = -16(t^2 - (67/16)t + 4489/1024 - 4489/1024)
    = -16( (t - 67/32)^2 - 4489/1024)
    = -16(t - 67/32)^2 + 4489/64

    it will reach the maximum height at 67/32 or appr 2.09 sec, and that max height is 4489/64 or 70.14 ft

    Notice we could have used the properties of the parabola to shorten this up a bit
    since the x-intercepts are 0 and 4.19, the vertex must lie midway between them
    This would be 2.09 , the answer I got when completing the square. Subbing 2.09 in for f(2.09) gives us
    -16(2.09)^2 + 67(2.09) = 70.14

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