SOLUTION: The height h in feet of an object after t seconds is given by the function {{{h=-16t^2+90t+10}}} How long will it take the object to hit the ground?

Question 103994: The height h in feet of an object after t seconds is given by the function

How long will it take the object to hit the ground?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The object will hit the ground when the height is 0, so let 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=90, and c=10

Square 90 to get 8100

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 5.7 seconds for the object to hit the ground.
RELATED QUESTIONS
The height h in feet of an object after t seconds is given by the function... (answered by stanbon)

The height h in feet of an object after t seconds is given by the function h =... (answered by Nate)

Can someone show me how to do this problem with step by step instructions. Thank you The (answered by rapaljer,Earlsdon)

The height h in feet of an object after t seconds is given by the function h = �16t^2... (answered by jim_thompson5910)

The height h in feet of an object after t seconds is given by the function h = �16t^2... (answered by ankor@dixie-net.com)

The height h in feet of an object after t seconds is given by the function h = �16t^2... (answered by stanbon)

The height h in feet of an object after t seconds is given by the function... (answered by stanbon)

The height h in feet of an object after t seconds is given by the function h = �16t^2... (answered by stanbon)

The height h in feet of an object after t seconds is given by the function... (answered by stanbon)