SOLUTION: A rock is thrown upward at an initial velocity of 16 ft/sec from a height of 96 feet above ground. How long will it take to hit ground?

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Question 101961: A rock is thrown upward at an initial velocity of 16 ft/sec from a height of 96 feet above ground. How long will it take to hit ground?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The equation you are looking for is:
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H+=+-16t%5E2+%2B+V%5Bo%5Dt+%2B+H%5Bo%5D
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where the variables are defined as follows:
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H is the height of the rock at time "t" after it is launched
t is the time after launch
V%5Bo%5D is the velocity with which the rock is launched
H%5Bo%5D is the height above the ground from which the rock is launched.
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First V%5Bo%5D is given in the problem +16 ft/sec. The sign of this term is plus because the
rock is thrown upward. Next H%5Bo%5D is given in the problem as +96 ft. The sign of this
term is plus because the launch point is above the ground level. Substituting these two
values into the equation results in:
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H+=+-16t%5E2+%2B+16t+%2B+96
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One more thing. When the rock finally hits the ground, its height above the ground will
be zero. Therefore, substitute 0 as the value of H to make the equation:
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0+=+-16t%5E2+%2B+16t+%2B+96
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From here on, this is just a math exercise of solving a quadratic equation.
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Note that 16 is a factor of every term on the right side ... therefore, you can divide both
sides of this equation (all terms) by 16 and the result is:
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0+=+-t%5E2+%2B+t+%2B+6
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To get this in a little more standard form, transpose the equation by switching sides, and
then multiply the entire equation by -1. When you do that you get:
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t%5E2+-+t+-+6+=+0
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This can be factored to:
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%28t+-+3%29%2A%28t+%2B+2%29+=+0
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Notice that this equation will be true if either of the factors is zero because multiplication
by zero on the left side will make the left side equal to the 0 on the right side.
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So we can find the two possible answers for t by setting each of the factors equal to zero
to get:
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t+-+3+=+0
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and
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t+%2B+2+=+0
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The first is solved by adding 3 to both sides to get t+=+3. The second is solved by
subtracting 2 from both sides to get t+=+-2. This second solution can be ignored because
a minus value of time means a time before launch. The answer, therefore, is t = 3 seconds.
That means that 3 seconds after the launch of the rock (with an initial upward velocity of
16 ft/sec from a height of 96 ft) the rock will hit the ground.
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Hope this helps you to understand how to set up the problem and then how to solve it.
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