SOLUTION: a fairgrounds most popular attraction is a roller-coaster ride known as the terror run. one of the stretches of track is called the missile path and is in the form of a parabolic c

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Question 185580: a fairgrounds most popular attraction is a roller-coaster ride known as the terror run. one of the stretches of track is called the missile path and is in the form of a parabolic curve,starting at point A on the curve and ending at B. B is 180m horizontally from A and the highest point of the curve is 100m above A and B.
(a) what is the quadratic expression to describe the missile path ?
Answer by ankor@dixie-net.com(22740) (Show Source):
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missile path and is in the form of a parabolic curve, starting at point A on
the curve and ending at B. B is 180m horizontally from A and the highest
point of the curve is 100m above A and B.
:
(a) what is the quadratic expression to describe the missile path ?
:
The axis of symmetry will be 180/2 = 90; where it is at a max of 100 m
we have two sets of coordinates
x=90, y=100
x=180, y = 0
:
Using the form ax^2 + bx + c = 0
Assume the path starts at origin, 0,0; so c = 0
90^2a + 90b = 100
8100a + 90b = 100
and
180^2a + 180b = 0
32400a + 180b = 0
:
Solve for a and b; multiply 1st equation by 2, subtract from the 2nd eq
32400a + 180b = 0
16200a + 180b = 200
---------------------subtraction eliminates b
16200a = -200
a =
a = -.0123
:
Find b
8100(-.0123) + 90b = 100
-100 + 90b = 100
90b = 100 + 100
90b = 200
b =
b = 2.22
:
Equation would be: y = -.0123x^2 + 2.22x
:
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