What is the measured trajectory and amplitude when a horse jumps over a vertical fence?

 

Is there math involved in horse
jumping? Each time a horse jumps over different jumps with varying heights, the
trajectory of the jump from start to finish can be measured using several
different equations. When measuring trajectory in an object, there is a
specific formula to calculate the answer. This changes depending on the type of
object and situation being measured. With this question, height will be
measured, vertically. There are several equations that are part of the formula
to finding the trajectory. The formulas are as follows: and in order to calculate motion,
given

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In order to find the answer, one
must separate horizontal and vertical measurements. One must also calculate
launch velocity, angle of launch, height, peak, and time in order to find
trajectory. Each component of calculating trajectory has its own equations.
Typically in the sport of jumping there is a pre-determined course of several
jumps at varying heights that the riders objective is to complete in a certain
manner and order. Sometimes the rider knows the course before hand, but more
often than not a rider will find out the course right before the show.  There are several factors when riding a horse
in order to complete a jump. Finding the projected trajectory can be beneficial
to any rider attempting to jump a horse due to the fact that it can potentially
influence the riders decision making on timing, speed, and method used to
complete course. Because the jumps are typically at different heights, the
speed of the rider should be increased and or reduced accordingly. In the sport
riders use specific signals and commands to their horse to ask them to jump
over the jump. Knowing the proper timing component of trajectory is imperative
to successfully completing this process. 

In this particular field of
research, previously recorded averages are vitally important to consider as
each component of the problem changes every time. A standard speed and time
should be considered for each different height. 
The horses average size should also be considered, and the breed that’s
being measured and its average size as these numbers could change depending on
the breed. Thoroughbreds are often used as the quintessential jumping horse,
which stands at an average of 16 hands, and can travel at a approximately 44
miles per hour.

 

Materials

HorseTape
measure Computer
Arena
iphone

 

Background

An equestrian jumper must accomplish
two things to complete a jump in the air. They must be able to move their body
in a certain manner position and time, and to be able to sync their actions
with the horse they are riding. This takes a specific mathematical formula to
accomplish. When this happens simultaneously, when the formula is completed, the
jump is successful. Equestrian jumping includes hurdles in several different
fashions including: water,  walls and
rails, gates, brush and rales, post and rail, triple bars, rail and plank,
oxer, and wall.

There are several different aspects
to consider when gathering data for jumps. One must consider including: the
height of the fence, speed of the horse, the angle of elevation between the
horse and the jump, the time of contact, the time of flight, and the total
distance from the takeoff point to the landing of the horse on the two front
hooves. Each part includes many different parts that are needed to accomplish
them.  

Calculation

In order to calculate trajectory you
must find several things. You must have a “vertical position, (y), which can be
found with the equation  . You must calculate
the horizontal position(x), the initial velocity (V0), the acceleration due to
gravity (g), and the initial velocity.

The units are measured in (M) meters.

As complex as it is to calculate
trajectory, one can easily display the data using a simple parabola format.

Other factors to consider when
conducting these experiments are their weight and food consumption. Horses can
only consume 2.5% of their weight every day. Weight estimation can be
calculated with the formula: (g2l)/12,000. You must also consider
the size of the arena, and area around and between jumps otherwise known as
“jump spacing”.

In an experiment conducted to
calculate horse trajectory, the conductor attempted to display all these
categories and use the proper according formulas to display the results of the
recorded trajectory for horses.

 

 

 

 

 

 

 

 

 

 

This graphs show and display data in regards to different
heights and different types of jumps, and their following results in trajectory
accordingly. (Bochis Flavia). The same experimenter recorded data for one
specific jump, (vertical fence) and included it in several tables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

           

 

 

 

 

 

 

Results

This experimenter used several
different types of jumps and materials under (as controlled variables) to get a
more valid result. The validity is increased significantly when the land under
the jump is changed because it increases your data for multiple cases.
Additionally the experiments validity was increased as they used several
different types of jumps which is an advantage for the same reasons. However,
the only downfall that would weaken the validity is the fact that they used one
horse, and a horse will get increasingly tired as they progress in jumping.

Works Cited

Panara, Sawyer.
“Parabola of a Horse’s Jump.” Prezi.com,
28 May 2013, prezi.com/oykccdzrzqwa/parabola-of-a-horses-jump/.

http://www.spasb.ro/index.php/spasb/article/viewFile/1413/1363

http://www.softschools.com/formulas/physics/trajectory_formula/162/

 

 

 

 

 

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