Problema Solution
If a stone is tossed from the top of a 230 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 230, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
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Solution:
We equate the equation to 0 as ground represents a height of 0:
0 = -9.8t2 - 10t + 230
Using the quadratic formula, we have:
t = [10 ±√((-10)2 - 4(-9.8)(230))] / 2(-9.8)
t = -1.35 seconds
t = 4.36 seconds
Since a negative time is invalid, we only accept the positive answer. So we have:
t = 4.36 seconds