SOLUTION: a rock falls from a tower that is 176ft high. as it is falling , its height is given by the formula h=176-16t^2. how many seconds will take for the rocks to hit the ground (h=0)?

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Question 77320: a rock falls from a tower that is 176ft high. as it is falling , its height is given by the formula h=176-16t^2. how many seconds will take for the rocks to hit the ground (h=0)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we let h=0 then we get
0=176-16t%5E2
Now rearrange the quadratic in descending order
-16t%5E2%2B176=0
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%2B0t%2B176+=+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=%280%29%5E2-4%2A-16%2A176=11264.

Discriminant d=11264 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+11264+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%280%29%2Bsqrt%28+11264+%29%29%2F2%5C-16+=+-3.3166247903554
t%5B2%5D+=+%28-%280%29-sqrt%28+11264+%29%29%2F2%5C-16+=+3.3166247903554

Quadratic expression -16t%5E2%2B0t%2B176 can be factored:
-16t%5E2%2B0t%2B176+=+-16%28t--3.3166247903554%29%2A%28t-3.3166247903554%29
Again, the answer is: -3.3166247903554, 3.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B0%2Ax%2B176+%29



We must disregard the negative answer (a negative time doesn't make any sense), so our answer is
t=3.3166
So it takes about 3.3 seconds for the rock to hit the ground