SOLUTION: A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation h = -16 t^2 + 160 t + 270 models the ball's

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation h = -16 t^2 + 160 t + 270 models the ball's      Log On


   

Question 992194: A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation
h = -16 t^2 + 160 t + 270
models the ball's height \, h \, above the ground in feet, t seconds after it was thrown.
How high is the ball after 5 seconds?


How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation
h = -16 t^2 + 160 t + 270
models the ball's height h above the ground in feet, t seconds after it was thrown.
How high is the ball after 5 seconds?
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h(t) = -16t^2 + 160t + 270
Find h(5) = sub 5 for t.
h(5) is 670 feet.
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How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.
h(t) = -16t^2 + 160t + 270
-16t^2 + 160t + 270 = 0
Solve for t. Use the positive solution.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B160x%2B270+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28160%29%5E2-4%2A-16%2A270=42880.

Discriminant d=42880 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-160%2B-sqrt%28+42880+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28160%29%2Bsqrt%28+42880+%29%29%2F2%5C-16+=+-1.47108955277239
x%5B2%5D+=+%28-%28160%29-sqrt%28+42880+%29%29%2F2%5C-16+=+11.4710895527724

Quadratic expression -16x%5E2%2B160x%2B270 can be factored:
-16x%5E2%2B160x%2B270+=+%28x--1.47108955277239%29%2A%28x-11.4710895527724%29
Again, the answer is: -1.47108955277239, 11.4710895527724. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B160%2Ax%2B270+%29

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t = 11.5 seconds.
Maybe you didn't use the nearest 10th ?