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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B150x%2B5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28150%29%5E2-4%2A-16%2A5=22820.

Discriminant d=22820 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-150%2B-sqrt%28+22820+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+22820+%29%29%2F2%5C-16+=+-0.0332156501954231
x%5B2%5D+=+%28-%28150%29-sqrt%28+22820+%29%29%2F2%5C-16+=+9.40821565019542

Quadratic expression -16x%5E2%2B150x%2B5 can be factored:
-16x%5E2%2B150x%2B5+=+%28x--0.0332156501954231%29%2A%28x-9.40821565019542%29
Again, the answer is: -0.0332156501954231, 9.40821565019542. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B150%2Ax%2B5+%29

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