SOLUTION: A BATTER HITS A PITCHED BASEBALL WHEN IT IS 3 FEET OFF THE GROUND. AFTER IT IS HIT THE HEIGHT (IN FEET) OF THE BALL IS MODELED BY H=-16T^2+80T+3 WHERE T IS THE TIME ( IN SECONDS).

Question 119166: A BATTER HITS A PITCHED BASEBALL WHEN IT IS 3 FEET OFF THE GROUND. AFTER IT IS HIT THE HEIGHT (IN FEET) OF THE BALL IS MODELED BY H=-16T^2+80T+3 WHERE T IS THE TIME ( IN SECONDS). HOW LONG WILL IT TAKE THE BALL TO HIT THE GROUND? ROUND TO THE NEAREST HUNDEREDTH. H= 0. MAKE SURE THIS EQUATION IS IN STANDARD FORM.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The ball will hit the ground when h=0

Start with the given equation

Plug in h=0

Let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-16, b=80, and c=3

Square 80 to get 6400

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our possible solutions are:
or

However, since a negative time doesn't make sense, our only solution is

So it takes about 5.03 seconds for the ball to hit the ground.

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