SOLUTION: If a stone is tossed from the top of a 190 meter building, the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+190, where t is in seconds, and height is in m

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Question 387646: If a stone is tossed from the top of a 190 meter building, the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+190, 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+190
Set h(t) to zero and solve for t:
0=-9.8t^2-10t+190
0=-4.9t^2-5t+95
since we can't factor, we apply the quadratic formula. Doing so yields:
t = {-4.94, 3.92}
Tossing out the negative solution leaves us with:
t = 3.92 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=1887 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -4.94281767938234, 3.92240951611703. Here's your graph: