SOLUTION: An object that is falling or vertically projected into the air has its height, in feet, above the ground given by s=-16t^2+vot=so Where s is the height, in fee, vo is the original

Question 88736: An object that is falling or vertically projected into the air has its height, in feet, above the ground given by s=-16t^2+vot=so Where s is the height, in fee, vo is the original velocity of the object in feet per second, t is the time the object is in motion, is seconds, and so is the height in feet, from which the object is dropped or projected. The figure shows that a ball is thrown straight up from a rooftop at an original velocity of 80 feet per second from a height of 96 feet. The ball misses the rooftop on its way down and eventually strikes the ground. Use the formula and the infromation to solve problem 89-91 I am solving even #90
s=-16t^2+80t+96
t=4
s= -16(4^2)+80(4)+96
s= -16(16)+320+96
s=-256+320+96
s= 160ft

Ruchi: Correct solution, Darlene.
The equation for this problem is s=-16t^2+80t+96. Is there any way you can figure out how many seconds the ball will take to reach the ground?
I can't quite figure out how to set up this last question and solve it.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If we set the equation equal to zero, we can find out when the ball will hit the ground

So 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=96

Square 80 to get 6400

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

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph (just replace t with x), we get:

and we can see that the roots are and . This verifies our answer

Since a negative time doesn't make sense, so our only solution is . So it will take 6 seconds for the ball to hit the ground.
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