Question 132785This question is from textbook Fundamentals of Algebric Modeling
: An object is shot upward from a height of 96 feet with an intial velocity of 48 feet per second. Its height (h) above the ground in feet after t seconds is given by the formula
h = 16t^2 + 48t + 96 at what times will the object be 128 feet above the ground?
This question is from textbook Fundamentals of Algebric Modeling
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! An object is shot upward from a height of 96 feet with an intial velocity of 48 feet per second. Its height (h) above the ground in feet after t seconds is given by the formula
h = 16t^2 + 48t + 96 at what times will the object be 128 feet above the ground?
Let h = 128 feet above ground.
Then, 128 = 16t^2 + 48t + 96
We are looking for t.
So, let t = the time it will take the object to reach 128 feet above the rgound.
16t^2 + 48t + 96 - 128 = 0
16t^2 + 48t -32 = 0....This is a quadratic equation.
I really hate those big coefficient numbers. Do you see 16, 48 and 32?
Let's remove them!
I will divide all of them (including 0 on the right side) by 16, which is the coefficient of t^2.
Doing so, I get a simplified form of the quadratic equation:
t^2 + 3t -2 = 0....This is much easier to work with, right?
We factor the left side of the equation, if possible.
This quadratic equation is not factorable.
This means we must use the quadratic formula.
I assume that you know how to use it, right?
t = -b+ -sqrt{b^2 - 4ac})/2a, where a = 1, b = 3 and c = -2.
Plug and chug.
t = -3+ - sqrt{3^2 - 4(1)(-2)}/2(1)
t = -3 + -sqrt{9 + 8}/2
t = -3 + -sqrt{17}/2
We now separate t into two sections: a positive section and a negative section.
t = -3 + sqrt{17}/2
t = 0.561552813
The time it will take the object to reach 128 feet above the ground is about 0.6 seconds. I rounded to the tenths place.
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t = -3 - sqrt{17}/2
t = -3.561552813....This answer is rejected because we are dealing with measure of time, which always moves forward not backward and thus will always be positve.
Make sense?
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