In this issue of Math in the News we look at applications of math from the Sochi Olympics. Specficially we look at ski jumping and develop a quadratic model based on given data.

1. Sochi Math
Math in the News
Issue 91

2. #Sochi2014
Math abounds in the Olympics, whether it’s
data around Olympic records, medals won, or
other statistics. In this issue we will look at the
dramatic sport of ski jumping, and its
application to quadratics and other non-linear
models. Take a look at this interactive to learn
more about ski jumping (Source: NY Times).
http://www.nytimes.com/newsgraphics/2014/so
chi-olympics/ski-jumping.html

3. #Sochi2014
The path of the ski
jumper can be
approximated with a
parabola. From the
NY Times interactive
we learn that the skier
starts her jump 15 ft
off the ground and
can cover the length
of a football field. We
can sketch out a
model for this.

4. #Sochi2014
We get three
points: (0, 15), the
starting point,
(h, k), the vertex of
the parabola, and
(x, y) where the
skier lands. The
slant distance
covered is 300 ft.
and is the
hypotenuse of a
right triangle.

5. #Sochi2014
Use the Pythagorean Theorem to find the
horizontal distance.

6. #Sochi2014
You can now find the coordinates of the point
where the skier lands.

7. #Sochi2014
We now have two coordinates and can
conceive of the vertex of the parabola, (h, k).
From the video we see that the skier elevates
by about 3 ft. We can then assign a value to k.

8. #Sochi2014
The equation for a parabola in vertex form has
two variables, a and k, that are unknown. But
we do have two coordinates and can solve for
these two values.

9. #Sochi2014
Here is the solution using the first set of
coordinates. We end up with an equation that
shows a as a function of k.

10. #Sochi2014
Here is the solution using the second set of
coordinates. We end up with a second equation
that shows a as a function of k.

11. #Sochi2014
Substitute one equation into the other to solve
for h.

12. #Sochi2014
Substitute the value of h into one of the
equations to find a. We now have all the
parameters for the parabola in vertex form.

13. #Sochi2014
Here is the graph of the parabola, with two key
coordinates shown.

14. #Sochi2014
Now that you’ve seen how to construct a
quadratic model using curve-fitting techniques,
expand on your work:
• Try different values for k to see what impact
it has on how far the ski jumper jumps.
• Try a longer slant height to see what the
equation is for different values of k.