SOLUTION: 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoit

Question 93468: 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoity is 204ft/sec, the height is given by h=-16t^2+204t+28 When will the projectile hit the ground?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

To find out when the projectile will hit the ground, let h=0 and solve for t

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=204, and c=28

Square 204 to get 41616

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

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

So the projectile will hit the ground at about 12.89 seconds
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