SOLUTION: Can someone help me with this problem i have no idea where to even start. The height "h" in feet of an object after "t" seconds is given by the function h = -16t^2+70t+8 H

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Can someone help me with this problem i have no idea where to even start. The height "h" in feet of an object after "t" seconds is given by the function h = -16t^2+70t+8 H      Log On


   

Question 78020: Can someone help me with this problem i have no idea where to even start.
The height "h" in feet of an object after "t" seconds is given by the function
h = -16t^2+70t+8
How long will it take the object to hit the ground? Round the answer to the nearest thousandth.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To figure out when the object will hit the ground, let h=0 and solve for t. This means we can use the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B70x%2B8+=+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=%2870%29%5E2-4%2A-16%2A8=5412.

Discriminant d=5412 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-70%2B-sqrt%28+5412+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2870%29%2Bsqrt%28+5412+%29%29%2F2%5C-16+=+-0.11144676971869
x%5B2%5D+=+%28-%2870%29-sqrt%28+5412+%29%29%2F2%5C-16+=+4.48644676971869

Quadratic expression -16x%5E2%2B70x%2B8 can be factored:
-16x%5E2%2B70x%2B8+=+-16%28x--0.11144676971869%29%2A%28x-4.48644676971869%29
Again, the answer is: -0.11144676971869, 4.48644676971869. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B70%2Ax%2B8+%29


Ignoring the negative time, we get
t=4.49
So the object will hit the ground at about 4.49 seconds