Geogebra — Ladies’ Snowboard Slopestyle Jump Calculation

Final Jamie Anderson Wins Gold | Sochi 2014 Winter Olympics GeoGSeries# Episode #02

Gif 1. Jamie Anderson, the 2014 slopestyle gold medalist and the most decorated slopestyle snowboarder in U.S. history; source: https://youtu.be/pkiYGpAHHFc

Fig 1. Composite image by Jeremy White Source:https://www.nytimes.com/interactive/2018/02/12/sports/olympics/jamie-anderson-gold-slopestyle.html

Fig 2. Here is the equations: (RED) f(x) = -0.02x² + 1.22x — 0.25 and (BLUE) g(x) = -0.6x + 33.5

Hi, Let’s do the Math?

01#step — First thing first, open your Geogebra Classic.

Come on, move on, this will take just 3 minutes :)

02#step — Go to this link, and save the image to your desktop (hint: click Google image) or download from the link below ;)

03#step — Drag it to the Geogebra canvas:

Fig 3. Dragging the image to the Geogebra canvas

04#step — Redimensioning the image to 50 x_scales:

Fig 4. Stretching the image to scale it up

05#step — Right Mouse click, Go to Settings > Color > Opacity, and set it to 50%:

Fig 6. Setting > Color > Opacity

06#step — Click on Menu > Points and make A → Q points:

Fig 7. Making a bunch of points

07#step — Now make a List(<Points>):

Type:
l1 = {A,B,C,D,E,F,G,H,I,K,L,M,N,O,P,Q}

Easy:oOpen a brakets { anLetters in; then close brakets } hit Enter

08#step — Make the First equation: Quadradic Function:

Type:
FitPoly(l1)
Enter

09#step — Now, the last Function: Line Function:

Type:
-0.6 x+33.5
Enter

10#step — Enjoy the result:

f(x) = -0.02x² + 1.22x — 0.25
Type:
Root(f(x))
R = (0.21, 0) -> Landing point
S = (50.81, 0)-> Take off point 
Extremum(f(x))
T = (25.51, 15.27) -> Zenith point: the highest point reached in the heavens:)
g(x)=-0.6 x+33.5
Slope = -0.6

Yep, she goes up to 15.27 meters and jumps roughly 50.81 meters away. The slope is -0.6. What an achievement! (see T, R, and S yellow points below)

Fig 10. The complete graphics! see T, R, and S yellow points. Enjoy! Geogebra link.

Gold medal!

Fig. 9. The Winners! Sochi 2014 Winter Olympics; source: https://youtu.be/pkiYGpAHHFc

If you want to know more about this project, please kindly visit this presentation Explore Graphing Calculator and Geometry Apps (Part 1) from https://www.youtube.com/user/GeoGebraChannel.

Now let’s see Men’s Long Jump:

Gif 2. The top 3 in the Men’s Long Jump at the 2014 Adidas Grand Prix on 14th June. 1. Jeff Henderson (USA): 8.33m (MR) 2. Christian Taylor (USA): 8.06m 3. Rushwal Samaai (RSA): 8.00m; Source: https://youtu.be/lulSuX8kFQY

Fig 10. Kinematic model of flight and landing photo composition; Source: https://www.sciencephoto.com/media/320529/view/long-jump

Fig 11. Kinematic model of flight and landing: the equation is: (RED) f(x) = -0.09x² + 0.53x+ 2.05; Geogebra file link.

f(x) = -0.09x² + 0.53x + 2.05
Type:
Root(f(x))
B = (-2.69, 0) -> Landing point
P = (8.67, 0.03)-> Take off point
Extremum(f(x))
T = (3.03, 2.86) -> Zenith point: the highest point reached in the heavens:)

Yep, he goes up to 2.86 meters and jumps roughly 8.67 meters away. What an achievement! (see P and Q yellow points above)

That’s it!

If you want to know more about this project, please kindly visit this presentation Kinematic and Biodynamic Model of the Long Jump Technique By Milan Čoh, Milan Žvan, and Otmar Kugovnik.

Creativity is a skill that’s in demand.

Boost yours with these tips :)

See you around…

Bye!

Credits & References:

Explore Graphing Calculator and Geometry Apps (Part 1) from https://www.youtube.com/user/GeoGebraChannel

How Jamie Anderson Won Her Second
Straight Olympic Gold in Slopestyle by nytimes.com

JAMIE ANDERSON DOUBLES DOWN AT WORLD CHAMPIONSHIP OF SNOWBOARDING by gopro.com

Ski jumping by wikipedia.org

SO WHAT EXACTLY IS BIG AIR SNOWBOARDING? EVERYTHING YOU NEED TO KNOW AHEAD OF ITS OLYMPIC DEBUT by teamusa.org

Kinematic and Biodynamic Model of the Long Jump Technique by By Milan Čoh, Milan Žvan and Otmar Kugovnik

Men’s Long Jump by https://youtu.be/lulSuX8kFQY

Best Long Jumpers of all Time (2020)｜Top 29 List｜HD by https://youtu.be/85ba0ZZB7sE

Download File:

Zenith Point — Gold Medals — Snowboarding Jump Calculation

GeoGebra Classic - GeoGebra

Kinematic and Biodynamic — Long Jump

GeoGebra Classic - GeoGebra

Images

Google Drive link

Related Posts:

01# Episode — GeoGSeriesRegular Polygons & GeoGebra — Kids, No More Shame! GeoGebra Comes To School!

02# Episode —Geogebra — Ladies’ Snowboard Slopestyle Jump Calculation — Final Jamie Anderson Wins Gold | Sochi 2014 Winter Olympics (this one, for while:)

More About Parabola (2 Formulas):

Parabola_ax^2+bx+c

Parabola_(x-a)^2 = p(y-b)

f(x) = -0.02x² + 1.22x - 0.25 - Wolfram|Alpha

Keep striving! Never Settle!

J3