SOLUTION: If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it ta

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Question 313615: If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it take the ball to pass through a height of 120 ft on the way back down to the ground?

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it take the ball to pass through a height of 120 ft on the way back down to the ground?
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h = -16t^2 + 96t + 5
120 = -16t^2 + 96t + 5 solve for t
-16t^2 + 96t + 5 = 120
-16t^2 + 96t + -115 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=1856 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.65370879821637, 4.34629120178363. Here's your graph:

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t = 1.65 seconds going up
t = 4.346 seconds falling
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