SOLUTION: h = �16t^2 + vt + c The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per secon

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Question 747342: h = �16t^2 + vt + c
The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per second, and c is the starting height in feet.
If Adam, who is 6 feet tall, threw his baseball 80 feet per second straight up into the air, which of the following answers is the best estimate of how long it took the ball to come back to the ground?
I think this is the equation, h= -16t^2+80t+6
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
h= -16t^2+80t+6 (is correct)
.
when the ball is on the ground, h is zero. So, set h to zero and solve for t:
0 = -16t^2+80t+6
0 = 16t^2-80t-6
0 = 8t^2-40t-3
solve using the "quadratic formula" yields:
x = {5.07, -0.07}
throw out the negative value (extraneous) leaving
x = 5.07 seconds
.
Details of quadratic formula follows:

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=1696 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.07390753524675, -0.0739075352467502. Here's your graph: