SOLUTION: Time in the air. A ball is tossed into the air from a height of 12 feet at 16 ft/sec. How long does it take to reach the earth?

Question 321378: Time in the air. A ball is tossed into the air from a height
of 12 feet at 16 ft/sec. How long does it take to reach the
earth?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Time in the air. A ball is tossed into the air from a height
of 12 feet at 16 ft/sec. How long does it take to reach the
earth?
-----------
Acceleration due to gravity on Earth is ~-16ft/sec/sec. Negative because it's down.
Height as a function of time is
h(t) = -16t^2 + vt + h0, t in seconds, h in feet
v is the initial velocity, 16 ft/sec and h0 is the initial height, 12 feet
h(t) = -16t^2 + 16t + 12
It impacts when h = 0
-16t^2 + 16t + 12 = 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=1024 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.5, 1.5. Here's your graph:

-------------
Ignore the -0.5 seconds
t = 1.5 seconds

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