What is the connection between this question (refer to NCERT page no. 119) and the one about the 400 m athletics track (given in NCERT on page no. 118)?                                                                                                  [Page No. 119]

The two questions are essentially the same. To determine the staggered starting positions in a race, organisers must calculate how much longer an outer lane is than an inner lane. This extra distance comes entirely from the curved (semicircular) sections of the track.

Since finding the length of a curved section involves finding the circumference of a circle, the problem reduces to a circle-perimeter problem. The circumference of a circle is $C = 2\pi r$.

Therefore, the extra distance between two lanes is $2\pi r_2 - 2\pi r_1 = 2\pi(r_2 - r_1)$

This shows that the additional distance depends only on the difference between the radii of the lanes.

So, the track-stagger problem is really an application of the circumference of a circle. That is why we first need to learn how to calculate the perimeter (circumference) of a circle before solving such race-track problems.

$$C = 2\pi r$$

This key relationship explains both the length of a circular path and the staggered starts used in athletics tracks.