SOLUTION: Solving a science application. the height h in feet of an object after t seconds is given by the function. h= -16t^2+30t+7 how long will it take the object to hit the ground

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The object will hit the ground when h=0


Start with the given equation



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=30, and c=7



Square 30 to get 900



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 the possible solutions are:
or


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




So it takes about 2.085 seconds for the object to hit the ground.