SOLUTION: The height h in feet of an object after t seconds is given by the function
h = 16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the ne
Algebra.Com
Question 124287: The height h in feet of an object after t seconds is given by the function
h = 16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the nearest thousandth
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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=3
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 our possible solutions are:
or
However, since a negative time doesn't make sense, our only solution is
So the object will hit the ground at about 1.970 seconds
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