Question 1 of 42intermediate🔍 AnalyzeShort Answer2 marks

In my school, the playground is too small to have a 400 m track, so the school constructed a 200 m track instead. Does this mean that we need a smaller stagger for the race tracks in my school (i.e., smaller than the stagger used in the Olympics), for the same 4×1004 \times 100 m relay race?

Correct Answer

No, a smaller stagger is not needed for the 200 m track. The stagger is the distance between the starting points of adjacent lanes, used to compensate for the extra distance covered on the curved portions by runners in outer lanes.

While runners cover the same distance on straight stretches, those in outer lanes run further on curves because their semicircles have a larger radius. The required stagger depends on the difference in radius between adjacent lanes, which is determined by the lane width.

Since the lane width remains the same, the difference in the length of the curved paths for each lane does not change, regardless of the track's total length. Thus, the stagger for the 4×1004 \times 100 m relay will be the same.

Exercise: Think and Reflect | Q: 1 | (Page 1)
For More Understanding

Explanation

The textbook context explains that staggers are required to compensate for the greater distance covered on the curved portions of the track by runners in outer lanes, as their semicircles have a larger radius. The difference in distance between adjacent lanes depends solely on the difference in their radii, which is equal to the lane width (1.22 m in the given example). Because the lane width remains constant, the difference in the length of the curved paths also remains constant, irrespective of whether the total track length is 400 m or 200 m. Therefore, the required stagger for each 100 m segment of the relay will be identical to that of an Olympic track.

Solution Steps

  1. Step 1: Identify that the stagger compensates for the extra distance run on the curved portions by athletes in outer lanes.

  2. Step 2: Note that on straight stretches, runners cover the same distance, but on curves, the outer lane runner covers more distance due to a larger radius.

  3. Step 3: Establish that the stagger depends on the difference in radius between adjacent lanes (which equals the lane width), not the total length of the track.

  4. Step 4: Conclude that since the lane width is the same, the stagger required for the 4×1004 \times 100 m relay on a 200 m track is the same as that on a 400 m track.

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