Question 111951
If a rock is thrown upward with an initial velocity of 64 ft/second from the top of a 25-foot building.
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1) write the hight (s) equation using this information.
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This will be a quadratic equation: s = -16t^2 + 64t + 25
S is the height after t seconds
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The three terms of the above equation represent:
-16t^2: the force of gravity, negative because it's pulling down
64t: the velocity of the rock thrown upward, positive because it is going up
25: the height of the building where all this takes place
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2) how high is the rock after one second?
Substitute 1 for t in the equation and find s
s = -16(1^2) + 64(1) + 25
s = -16 + 64 + 25
s = 73 ft after 1 second
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3) after how many seconds will the graph reach maximum height?
This will occur at the axis of symmetry: Remember x = -b/(2a)
t = -64/2(-16)
t = -64/-32
t = + 2 seconds
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4) what is the maximum height?
This occurs when t = 2; substitute 2 for t in the equation, find s
s = -16(2^2) + 64(2)+25
s = -16(4) + 128 + 25
s = -64 + 128 + 25
s = +89 ft is the maximum

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A graphical presentation would be:
{{{ graph( 300, 200, -2, 6, -10, 100, -16x^2+64x+25) }}}
Y axis is the height and x axis is the time in seconds