''Impossible'' Question of parabola:
Q.
In a children’s playground there is a rope hanging from two points, A and B, on a horizontal beam.
A and B are 6 metres apart. The lowest point of the rope is 1 m above the ground.
The shape of the rope can be modelled by y = (x/3)(x – p) + 4
where y is the height above the ground, and x is the distance from A.
(i) How high above the ground is A?
(ii) Give the value of p.
(iii) On the grid, sketch the graph that models the shape of the rope.
(iv) Holes are drilled through a 2 m long horizontal board.
The rope passes through the holes to make the seat of a swing.
The height of the seat is 1.2 metres above the ground.
How far apart would the holes in the board need to be if the shape of the rope above the seat stays the same?
Give your answer to 2 dp. [decimal places]
can you solve this question: ?
.
.
.
.answer:-
(i) How high above the ground is A?
At the point A, the distance from A is 0 = x. Substitute the value:
y = (0/3)(0 – p) + 4 = 4
The point A is 4 metres* off the ground.
(*I put a “foot” in my mouth in the original post and said “feet.” I corrected this to metres thanks to a comment from Maarten.)
(ii) Give the value of p.
The point B is 6 = x metres away from A, and it is also the same 4 metres off the ground. Substitute (4, 6) into the equation:
4 = (6/3)(6 – p) + 4
0 = 2(6 – p)
0 = 6 – p
p = 6
(iii) On the grid, sketch the graph that models the shape of the rope.
The point A is (0, 4), the point B is (6, 4), and the lowest point is halfway and a height of 1, which is (3, 1). So we sketch a parabola connecting these three points.
(iv) Holes are drilled through a 2 m long horizontal board…[rest of question omitted]
We want to solve for the distance between the two holes, which is the same as solving for the difference of x values when y = 1.2.
If 1.2 = y, let’s solve for the two x values.
1.2 = (x/3)(x – 6) + 4
0 = (x/3)(x – 6) + 2.8
0 = x(x – 6) + 8.4
0 = x2 – 6x + 8.4
Now we can use the quadratic equation and find the difference between the two roots, |x1 – x2|.
So the answer is √2.4 ≈ 1.55.
What do you think? Did you figure it out, and was it too hard for 15 year olds?
By-vikash rahii
Q.
In a children’s playground there is a rope hanging from two points, A and B, on a horizontal beam.
A and B are 6 metres apart. The lowest point of the rope is 1 m above the ground.
The shape of the rope can be modelled by y = (x/3)(x – p) + 4
where y is the height above the ground, and x is the distance from A.
(i) How high above the ground is A?
(ii) Give the value of p.
(iii) On the grid, sketch the graph that models the shape of the rope.
(iv) Holes are drilled through a 2 m long horizontal board.The rope passes through the holes to make the seat of a swing.
The height of the seat is 1.2 metres above the ground.
How far apart would the holes in the board need to be if the shape of the rope above the seat stays the same?
Give your answer to 2 dp. [decimal places]
can you solve this question: ?
.
.
.
.answer:-
(i) How high above the ground is A?
At the point A, the distance from A is 0 = x. Substitute the value:
y = (0/3)(0 – p) + 4 = 4
The point A is 4 metres* off the ground.
(*I put a “foot” in my mouth in the original post and said “feet.” I corrected this to metres thanks to a comment from Maarten.)
(ii) Give the value of p.
The point B is 6 = x metres away from A, and it is also the same 4 metres off the ground. Substitute (4, 6) into the equation:
4 = (6/3)(6 – p) + 4
0 = 2(6 – p)
0 = 6 – p
p = 6
(iii) On the grid, sketch the graph that models the shape of the rope.
The point A is (0, 4), the point B is (6, 4), and the lowest point is halfway and a height of 1, which is (3, 1). So we sketch a parabola connecting these three points.
(iv) Holes are drilled through a 2 m long horizontal board…[rest of question omitted]
We want to solve for the distance between the two holes, which is the same as solving for the difference of x values when y = 1.2.
If 1.2 = y, let’s solve for the two x values.
1.2 = (x/3)(x – 6) + 4
0 = (x/3)(x – 6) + 2.8
0 = x(x – 6) + 8.4
0 = x2 – 6x + 8.4
Now we can use the quadratic equation and find the difference between the two roots, |x1 – x2|.
So the answer is √2.4 ≈ 1.55.
What do you think? Did you figure it out, and was it too hard for 15 year olds?
By-vikash rahii
''Impossible'' question releated to PARABOLA.
![''Impossible'' question releated to PARABOLA.]()
Reviewed by biharishayar
on
December 06, 2017
Rating:
Really sir
ReplyDeleteExcellent
Thanks dude.
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