SOLUTION: The height h in feet of an object after t seconds is given by the function h = �16t^2 + 70t + 4. How long will it take the object to hit the ground? Round your answer to the

Question 89292: The height h in feet of an object after t seconds is given by the function
h = �16t^2 + 70t + 4.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Please provide the step by step process. Thank you in advance for your help.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Set h equal to zero

Now 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=4

Square 70 to get 4900

Multiply to get

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

Simplify the square root

Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

or

which split up to

or

and simplify to

or

Which approximate to

or

Since a negative time doesn't make sense, we must discard the first solution.

So our solution is

which rounds to

So it will take close to 4 and a half seconds to reach the ground

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