SOLUTION: Hi, Can anyone help with this word problem? The height h in feet of an object after t seconds is given by the function h = –16t2 + 20t + 5. How long will it take the object to hit

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Hi, Can anyone help with this word problem? The height h in feet of an object after t seconds is given by the function h = –16t2 + 20t + 5. How long will it take the object to hit      Log On


   

Question 80866: Hi, Can anyone help with this word problem? The height h in feet of an object after t seconds is given by the function h = –16t2 + 20t + 5. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find when it will hit the ground, set h equal to zero

0+=+-16t%5E2+%2B+20t+%2B+5

Now use the quadratic formula to solve for t

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B20t%2B5+=+0) has the following solutons:

t%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=%2820%29%5E2-4%2A-16%2A5=720.

Discriminant d=720 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+720+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2820%29%2Bsqrt%28+720+%29%29%2F2%5C-16+=+-0.213525491562421
t%5B2%5D+=+%28-%2820%29-sqrt%28+720+%29%29%2F2%5C-16+=+1.46352549156242

Quadratic expression -16t%5E2%2B20t%2B5 can be factored:
-16t%5E2%2B20t%2B5+=+-16%28t--0.213525491562421%29%2A%28t-1.46352549156242%29
Again, the answer is: -0.213525491562421, 1.46352549156242. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B20%2Ax%2B5+%29



Ignoring the negative answer, the answer is:

t=1.46352549156242