SOLUTION: A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in t seconds is given by s(t)=-16(t^2)+142t. At what time(s) will the ball be 172 ft fr

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Question 166879: A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in t seconds is given by s(t)=-16(t^2)+142t. At what time(s) will the ball be 172 ft from the ground?
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
s(t)=-16(t^2)+142t
.
In this case, they are saying that if s(t) equals 172 feet what is t?
.
Simply set s(t) to 172 and solve for 't':
s(t)=-16(t^2)+142t
172=-16(t^2)+142t
16(t^2)-142t+172=0
8(t^2)-71t+86=0
.
Since it is difficult to factor, we use the quadratic equation.
Doing so will yield:
x = {7.428, 1.447}
Units are in seconds
.
Here's the quadratic equation:
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=2289 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7.42771842847642, 1.44728157152358. Here's your graph:
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