Three athletes P, Q and R run on three separate circular tracks of radii 120m, 150m and 200m respectively. Starting from the same radial line, they run such that P turns through 90∘, Q through 70∘ and R through 50∘.
(i) Calculate the distance covered by each athlete along his or her track.
(ii) Rank the distances in descending order and support your ranking with numerical values.
(iii) Determine by what percentage the longest distance exceeds the shortest.
(iv) If all three athletes now wish to cover exactly 300m along their respective tracks, compute the angular displacement required for each and identify who needs to turn through the greatest angle.