SOLUTION: If a stone is tossed from the top of a 310 meter building, the height of the stone as a function of time is given by h(t) = -9.8t^2 – 10t + 310, where t is in seconds, and height

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Question 387214: If a stone is tossed from the top of a 310 meter building, the height of the stone as a function of time is given by h(t) = -9.8t^2 – 10t + 310, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
h(t) = -9.8t^2 – 10t + 310
Set h(t) to zero (since when height = 0, it'll hit the ground):
0 = -9.8t^2 – 10t + 310
since we can't factor, we apply the "quadratic formula". Doing so yields:
x = {-6.16, 5.14}
We can toss out the negative solution leaving:
x = 5.14 seconds
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=12252 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -6.15758942939662, 5.13718126613131. Here's your graph:
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