# SOLUTION: Science and medicine. 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

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Science and medicine. 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       Log On

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 Question 81550: Science and medicine. 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.Answer by ankor@dixie-net.com(15652)   (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