Question 75290: The equation h=-16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.
Please show work
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The equation h=-16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.
:
Substitute 180 for h in the given equation: -16t^2 + 112t = h
:
-16t^2 + 112t = 180
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-16t^2 + 112t - 180 = 0; subtract 180 from both sides, gives us a quadratic eq:
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Simplify divide equation by -4, that changes the signs and gives you:
4t^2 - 28t + 45 = 0
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Factor this to:
(2t - 5)(2t - 9) = 0
:
2t = +5
t = 2.5 sec (on the way up)
and
2t = +9
t = 4.5 sec (on the way down)
:
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Check solution using t = 2.5, in the original equation:
-16(2.5^2) + 112(2.5) =
-16(6.25) + 280 =
-100 + 280 = 180
:
You can check it using the t = 4.5 solution
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