SOLUTION: Suppose Charlie hit a baseball straight upward at 150 ft/sec from a height of 5 ft. Use the formula to determine how long it takes the ball to return to the earth. (If an objec

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Question 207392This question is from textbook Elementary and Intermediate Algebra
: Suppose Charlie hit a baseball straight upward at 150 ft/sec from a height of 5 ft. Use the formula to determine how long it takes the ball to return to the earth.
(If an object is given an initial velocity of vo ft per second from a height of so ft, then its height S after t secondsis given by the formula S = -16t^2 +vo t + so.)
With that, I came up with the equation S = -16t^2 + 150t + 5. I think that's right, but I'm not positive...then I'm not sure how to solve either. I appreciate any help!! :) This question is from textbook Elementary and Intermediate Algebra

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
S = -16t^2 + 150t + 5
It's the right formula. It's usually height as a function of time,
h(t) = -16t^2 + 150t + 5
---------------
When it hits the ground, h = 0
0 = -16t^2 + 150t + 5
-16t^2 + 150t + 5 = 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=22820 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.0332156501954231, 9.40821565019542. Here's your graph:

The solver uses x, just sub that for t.
The negative value is ignored.
t =~ 9.4082 seconds

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