SOLUTION: A baseball is thrown upward with an initial speed of 69ft/sec. The number of feet s above the ground after t seconds is given by the equation s=-16t^6+69t. When will the baseball b

Question 213153: A baseball is thrown upward with an initial speed of 69ft/sec. The number of feet s above the ground after t seconds is given by the equation s=-16t^6+69t. When will the baseball be 54 feet above the ground?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The problem gives you:
s=-16t^6+69t
.
Where s = feet above ground
.
Now, they would like to know at what time (t) is it when it is 54 feet above the ground. Simply substitute s for 54 and solve for t:
s=-16t^6+69t
54=-16t^6+69t
0=-16t^6+69t-54
0=16t^6-69t+54
Solve by using the quadratic formula. Doing so yields:
t = {3.285, 1.027} (in seconds)
The reason for two answers -- once going up and another time coming down.
.
Details of quadratic below:

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=1305 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.28514949176178, 1.02735050823822. Here's your graph:

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