Question 599432
If a stone is thrown upward from a height of 8.25 feet with an initial velocity of 64 feet per second, how long does it take for the stone to fall to the ground? Give answer to the nearest one-hundredth. (Formulas: ; where h represents final height, is initial velocity, t is time and is the initial height)
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General formula:
h(t) = -32t^2 + vt + Ho
where
h(t) is height at time t
t is time (secs)
v is initial velocity
Ho is the initial height
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From stated problem, then, we have:
h(t) = -32t^2 + 64t + 8.25  (formula)
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how long does it take for the stone to fall to the ground?
set h(t) to zero and solve for t:
h(t) = -32t^2 + 64t + 8.25
0 = -32t^2 + 64t + 8.25
applying the quadratic formula, we get
t = {-0.12, 2.12}
we can throw out the negative solution (extraneous) leaving:
t = 2.12 seconds
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Details of quadratic to follow:
*[invoke quadratic "x", -32, 64, 8.25 ]