SOLUTION: A model rocket is launched from a height of 96 feet. The formula h=-16t^2+80t+96 describes the rockets height, h, in feet, t seconds after it was launched. How long will it take th

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Question 27374: A model rocket is launched from a height of 96 feet. The formula h=-16t^2+80t+96 describes the rockets height, h, in feet, t seconds after it was launched. How long will it take the rocket to reach the ground?
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
This is a basic quadratic equation exercise. We want to find the t at which the rocket hits the ground. The fact that it hits the ground implies that the its height is now zero. So we must solve the equation:
-16t%5E2%2B80t%2B96+=+0
We use the standard procedure:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B80x%2B96+=+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=%2880%29%5E2-4%2A-16%2A96=12544.

Discriminant d=12544 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-80%2B-sqrt%28+12544+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2880%29%2Bsqrt%28+12544+%29%29%2F2%5C-16+=+-1
x%5B2%5D+=+%28-%2880%29-sqrt%28+12544+%29%29%2F2%5C-16+=+6

Quadratic expression -16x%5E2%2B80x%2B96 can be factored:
-16x%5E2%2B80x%2B96+=+%28x--1%29%2A%28x-6%29
Again, the answer is: -1, 6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B80%2Ax%2B96+%29


The two solutions are -1 and 6, but since time cannot be negative, the relevant solution is 6. The rocket hits the ground 6 seconds after it's launched.