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Parabolas & Horse Jumping

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by

Courtney Vander Werf

on 28 April 2014

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Transcript of Parabolas & Horse Jumping

How do Parabola's fit in?
I chose to focus specifically on a horse's jump and how it creates a parabola. However, before I get into that, first you need to understand the basics of jumping!
The Parabola in Relation to the Jump
Peak (Mid Flight)represents the vertex.
Take off and Landing points represent the x-intercepts.
The relationship is always negative, or minimum.
Axis of Symmetry goes vertically through the highest point of the jump(not necessarily the center).
The equation represents the path of the horse's FEET.
Now, in motion
Math in the Equine World
There are many ways that math is used in the equine world:
Parabolas & Horse Jumping
Feeding
A horse can only consume about 2.5% of its body weight a day.
Ratios are used when mixing nutrients to make sure all the requirements are met.
A Proper Jump:
The take off and the landing are the same distance away from the fence. (a & e)
The peak is directly over the highest point of the fence. (c)
By: Courtney Vander Werf
Weighing
Estimating a horse's weight is a mathematical equation.
( x L)/12,000
Arenas
A competition Dressage arena must be 20m by 60m.
Pythagoras's Theorem is used to make sure the length and angles are correct.
Space between Jumps
When you put it all together, it starts to look like a parabola!
y=ax^2+bx+c
Info for Photos:
I found multiple photos of horses jumping and put each one on a graph. In each photo, the horse is at a different stage of their jump.
Axis of Symmetry was the common piece of information in each photo.
In all photos, the fence is visible.
If you know the highest point of the fence, then you know exactly where the axis of symmetry is.
If you know the take off, you know the landing.
With that single piece of information, you can find both x-intercepts.
In order to clear the jump, the parabola's vertex has to be greater than the highest point of the fence.
When the vertex is unknown, you can make an inequality to show where the vertex must be in order to have a successful jump.
The End
In show jumping, the number of horse strides determine the spacing between the jumps.
Full transcript