SOLUTION: Science and medicine. The equation {{{h= -16t^2+112t}}} gives the hight of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the

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Question 75838This question is from textbook Beginning Algebra
: Science and medicine. The equation h=+-16t%5E2%2B112t gives the hight 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.
This problem has me confussed and frustrated and need some help figuring this out. I am not sure what I am doing wrong. Please help. Thanks so much. This question is from textbook Beginning Algebra

Answer by ankor@dixie-net.com(22740) About Me  (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
:
-16t^2 + 112t - 180 = 0; subtract 180 from both sides, gives us a quadratic eq:
:
Simplify divide equation by -4, that changes the signs and gives you:
4t^2 - 28t + 45 = 0
:
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)
:
:
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