SOLUTION: Please help with this word problem. If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80 ft/s, its height h after t s is given by h=-16t^

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To find when it hits the ground, 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=80, and c=5



Square 80 to get 6400



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