Question 848716: Good old St.Nick needs your help getting from Nathan's house to Jack's house on Christmas Eve. Of course that means rooftop to rooftop. With your knowledge of parabolas,Santa has asked your to guide his sleigh. It is 300 feet between their rooftops and there is a really big tree halfway between their houses that stand 190 feet above the roof levels. If Santa must fly a parabolic path and he wants to just clear the tree, what would be the equation of the parabola that he would enter into his on-board computer.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Good old St.Nick needs your help getting from Nathan's house to Jack's house on Christmas Eve. Of course that means rooftop to rooftop. With your knowledge of parabolas,Santa has asked you to guide his sleigh. It is 300 feet between their rooftops and there is a really big tree halfway between their houses that stand 190 feet above the roof levels. If Santa must fly a parabolic path and he wants to just clear the tree, what would be the equation of the parabola that he would enter into his on-board computer.
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Draw the picture on an x/y coordinate plane.
The parabola passes thru (-150,0)(0,90)(150,0)
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Form: ax^2 + bx + c = y
Using -150,0 you get: 150^2a - 150b + c = 0
Using +150,0 you get: 150^2a + 150b + c = 0
Using 0,90 you get::: 0 + 0 + c = 90
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Solve for a,b,c ::
a = -0.004
b = 0
c = 90
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Equation:
y = -0.004x^2 + 90
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Cheers,
Stan H.
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