SOLUTION: The height h in feet of an object after t seconds is given by the function h = �16t^2 + 70t + 8. How long will it take the object to hit the ground? Round your answer to the

Question 96024: The height h in feet of an object after t seconds is given by the function
h = �16t^2 + 70t + 8.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find when it hits the ground, let h=0

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=70, and c=8

Square 70 to get 4900

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 will take about 4.486 seconds to hit the ground.
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