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# The Mathematics of Track & Field

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## Shani P

on 15 May 2013

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#### Transcript of The Mathematics of Track & Field

TRACK & FIELD What does the mathematics of
Track & Field mean? It's the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols but, in reference to this sport. http://www.thefreedictionary.com With around 30 different events based on jumping, running,throwing and walking, these various events fall under two categories... -This type of runners uses maximum effort for the entire race and need pure speed as well as a good starting-block technique to be successful.
-Sprints have a different starting process than longer events. How to Pace? - We find this by taking our goal of a 60 sec 400m and dividing it by four, because there are four, hundred-meter marks in a 400-meter dash, where each 100m would be run in 15 seconds.
- If we wanted to meet the same 60-second time, but create goals in 200-meter intervals, each 200 would have to be run in thirty seconds, dividing 60 by 2.
- These are called splits
- To take into consideration fatigue and stamina, we can adjust our goals to a fast time in the first two hundred meters of the race, and a slower two hundred meter time in the last homestretch.
- Example: Instead of two, 30 second, 200 meters, we could now make our goals to be a hard 28-second 200-meters, followed by a 32 second finishing 200. Speed When we speak about track, we often ask, “How fast did he or she run?” or questions such as, “What was her time?” To answer these kinds of questions we can use algebra.

For example, a 17-year-old female sprinter runs a 100-meter dash in 13 seconds, what is her speed in feet per second? d = rt
1 meter= 3.28084 ft
___1m___ = __100-meters _
3.28084 ft d feet
d= 328.084 feet Symmetry of the track Components:

- Two straight 100 meters
- Two curves
- Called an equal-quadrant for its shape How far does someone in lane 4 run one lap?

- Although our instincts would cause us to think the immediate answer is 400-meters, we work out the problem to get a different answer.
- The curves, causes us to run farther as we are further away from the inside metal rail.
- If we were to combine the two circles, we would have a circle with a circumference of 200-meters. To find the radius of this 200-meter circle we just configured we can manipulate the formula, C= 2πr. Staggered Starts There’s plenty of mathematics behind track, yet sometimes we have to think about it in-depth, such as we have done here. It never ends... Throwing Hammer Throwing Discus Throw Shot Put Javelin Throw Jumping High Jump Long Jump & Triple Jump P
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G Will math ever cease to exist in Track & Field?
By: Shani Paul What do you think???????????????? Even though my term paper focused more on the 400-meter event in the track section of Track and Field, it's key to remember that examples of mathematics in this sport are limitless. http://trackandfield.about.com/od/skillsrequired/p/sprintintro.htm PACE (distance (d) = 328.084)
(time (t) = 13)

r = __d__
t

___328.084 ft __ = 25. 24 ft/sec
13 sec C= 2πr
200m= 2πr

__200m__ = r

r = 31.83m 31.85m + 4m = 34.85m for lane 4

C= 2πr
= 2π (34.85)
C= 218.858m

- 218.86 m for the curves and 200 meters for the straights

437.716 m would be the distance one would run in the fourth lane. How does this work?
- At the beginning of a 400m race, each runner is staggered on the track to have a fair race.
- How far do we have to be staggered from one another on a 400m track in order for the distance run to be equal?
- While investigating the mathematics behind track, we realize even this we can compute this too and it serves as “Problem #3” that I investigate in my Term Paper. The results show that each lap increases equally around 6.3 meters. Therefore, in the 400m, it’s important that athletes remain in their respective lanes around the turns, so it’s sure that each competitor has run 400m. At the beginning of the race, the runners are staggered by this amount, to ensure the fairness of the event. Specifically, the athlete in the lane closer to the inner metal rail, would be staggered 6.3-meters behind the athlete in the lane farther away from the inside rail. This is in comparison to long distance races, where staying in one's lane isn't as crucial. www2.ohlone.edu/people2/bbradshaw/math155/text/m155_text_ch5.pdf THE END :)
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