SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the

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Question 69252: The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 30t + 3.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
I wish that I knew how to do this problem!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find out how long it will hit the ground set h equal to zero and solve for t
0+=+-16%2At%5E2%2B30%2At%2B3 Solve for t using the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B30t%2B3+=+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=%2830%29%5E2-4%2A-16%2A3=1092.

Discriminant d=1092 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+1092+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2830%29%2Bsqrt%28+1092+%29%29%2F2%5C-16+=+-0.095169477616144
t%5B2%5D+=+%28-%2830%29-sqrt%28+1092+%29%29%2F2%5C-16+=+1.97016947761614

Quadratic expression -16t%5E2%2B30t%2B3 can be factored:
-16t%5E2%2B30t%2B3+=+-16%28t--0.095169477616144%29%2A%28t-1.97016947761614%29
Again, the answer is: -0.095169477616144, 1.97016947761614. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B30%2Ax%2B3+%29

The second answer t=1.97016947761614 is the time it took to hit the ground at the point where h=0 (the negative answer doesn't make sense).