SOLUTION: The height h (in feet) of a rocket as a function of the time t (in seconds) of flight is given by the following equation. Determine the times t when the rocket is on the ground.

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Question 252831: The height h (in feet) of a rocket as a function of the time t (in seconds) of flight is given by the following equation. Determine the times t when the rocket is on the ground.

h=50+280t-16t^2
I have set up an equation but don't know if this is right. Also, I'm not understanding what they are asking or how to solve this. Please help me. Thank you.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The height h (in feet) of a rocket as a function of the time t (in seconds) of flight is given by the following equation. Determine the times t when the rocket is on the ground.
h=50+280t-16t^2
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It's on the ground when h = 0.
-16t^2 + 280t + 50 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B280x%2B50+=+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=%28280%29%5E2-4%2A-16%2A50=81600.

Discriminant d=81600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-280%2B-sqrt%28+81600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28280%29%2Bsqrt%28+81600+%29%29%2F2%5C-16+=+-0.176785535678562
x%5B2%5D+=+%28-%28280%29-sqrt%28+81600+%29%29%2F2%5C-16+=+17.6767855356786

Quadratic expression -16x%5E2%2B280x%2B50 can be factored:
-16x%5E2%2B280x%2B50+=+%28x--0.176785535678562%29%2A%28x-17.6767855356786%29
Again, the answer is: -0.176785535678562, 17.6767855356786. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B280%2Ax%2B50+%29

Ignore the negative value.
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PS I don't know why this is called a rocket, it has no thrust. It's a ballistic object, shot upward and goes up and back down due to gravity.