NCERT Solutions for Class 9th Maths Chapter 6 A Closer Look at a 400 m Athletics Track — Think and Reflect
Book page 127 Updated on2026-09-19
Q1.
What is the difference in radius between the first and second lanes? Use the Fig. 6.11 to find the stagger needed by the runner in the second lane. Will an equal stagger be needed between the third and second lanes?Fig. 6.11 — schematic diagram of a 400 m athletics track: eight lanes, two straights of 84.39 m each and two semicircular bends with common centres A and B. The innermost semicircle has radius 36.5 m and each lane is 1.22 m wide.
Answer
Difference in radius = 1.22 m (one lane width). Stagger ≈ 7.67 m, and yes, the same stagger is needed between lanes 2 and 3, and between every other adjacent pair.
Lane 1: the runner keeps 0.3 m out from the inner kerb, so r₁ = 36.5 + 0.3 = 36.8 m Lane 2: one lane further out, so r₂ = 36.8 + 1.22 = 38.02 m r₂ − r₁ = 1.22 m
Lap in lane 1 = 2 × 84.39 + 2π(36.8) = 168.78 + 231.22 = 400.00 m Lap in lane 2 = 2 × 84.39 + 2π(38.02) = 168.78 + 238.89 = 407.67 m
Stagger = 407.67 − 400.00 = 7.67 m
The same number comes out in one line without computing either lap:
Why it happens: the two straight sections are identical in every lane, so they cancel. The two bends of a lane together make one full circle, so the extra distance is the difference of two circumferences — and that difference depends only on the difference of the radii, never on how big the radii are. Since every pair of adjacent lanes differs by the same 1.22 m, every stagger is the same 7.67 m. That is why, in the photograph on the opening page, the starting marks climb up in equal steps.
Check it yourself: lane 8 is 7 lanes out from lane 1, so its start is 7 × 7.67 ≈ 53.7 m ahead — more than half the length of the straight.