## Monday, September 10, 2007

### 100-Meter Sprint/Dash -- a Source for Interesting Calculations

On Sept. 9, 2007, Asafa Powell broke his own 100-meter sprint/dash world record, his new record is now 9.74 sec. This race and his record can be a source for interesting calculations:

1. How many steps it takes the runners to cover 100 m?

2. What is the average step size?

3. What is their speed in terms of mph?

4. How much time during the race they spend in the air (as oppose to touching the ground)?

This can be evaluated/estimated by viewing the video frame by frame.

I believe it is more than half the time.

Look at it another way, with respect to distance, not time:
Most of the 100-meter distance he covers while he is airborne. If so, in a sense, with respect to distance, he is flying. But this is a misrepresentation because he must touch the ground every step in order to propel his airborne self for the next segment of his “flight.”

5. Assuming that Asafa Powell's weight is still 88 kg (per Wikipedia's older article), then:

5.1. What is his acceleration?

5.2. How much force he spent?

5.3. How much energy?

1. any answers? don't have a clue how to calculate this but would love to see how.

2. You need to watch a video of a 100-meter spring/dash (few are available.)

(1) The mathematical activities can start with counting how many steps it takes for a runner to cover 100 meters. In one video we saw, we counted 42 steps.

(2) Calculate the average length of a single step. In our example, dividing 100 meters by 42 steps: 100/42 we got 2.38 meter, which is approx. 7 ft. 10 inches. That's a single step. Try to make such a long step.

(3) Estimate the length of the steps at the very end of the race. Since the steps at the very beginning are shorter than the average, those at the very end must be longer.

(3.1) If you have access to an official race track, go measure the distance between the lines at the last few meters of the track, those that are perpendicular to the track lines. (Or find this data by some other research means.)

(3.2) Back with the video: use the measurements you did at the tack to estimate the length of a runner's single stride as he runs over these lines. Compare your results with the estimates you got in exercise #3.

(4) Measure how much time a runner spends touching the ground and subtract it from the time it took him to cover 100 meters. The result is how much time he spent in the air.

(4.1) Can you say he was flying? Explain your answer.

(4.2) What is the function of the runner's step touching the ground? [This and the following questions are actually science, physics, to be precise; you need math to answer questions in physics.]

(4.3) if you know the weight of the runner (you can find it out with a little research), then calculate:

(4.3.1) The force he applied at each step to propel himself forward.

(4.3.2) The energy he spent making each step.

(4.3.3) The energy he spent during the entire race.

(4.3.4) How much pasta or pizza he would have had to eat to get that many calories?

These are just a few examples.

Please post here if you or your students do any of these exercises, what are your/their results and what you/they learn.

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