SOLUTION: Solving a science application. the height h in feet of an object after t seconds is given by the function. h= -16t^2+30t+7 how long will it take the object to hit the ground

Question 119951: Solving a science application.
the height h in feet of an object after t seconds is given by the function.
h= -16t^2+30t+7
how long will it take the object to hit the ground? round nearest thousandth
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The object 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=30, and c=7

Square 30 to get 900

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 the possible solutions are:
or

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

So it takes about 2.085 seconds for the object to hit the ground.
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