Question:
In the 2024 Olympics, two runners, Noah Lyles and Kishane Thompson, finished the 100.00 m race in 9.784 s and 9.789 s respectively. Assuming that they move with constant speed throughout the race, the distance between the two runners when Noah Lyles touched the finishing line would be closest to:
In the 2024 Olympics, two runners, Noah Lyles and Kishane Thompson, finished the 100.00 m race in 9.784 s and 9.789 s respectively. Assuming that they move with constant speed throughout the race, the distance between the two runners when Noah Lyles touched the finishing line would be closest to:
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For races involving nearly equal finishing times, calculate the time difference first and then multiply it by the speed of the slower athlete. This provides the separation at the moment the winner finishes.
Updated On: Jun 11, 2026
- 5 cm
- 10 cm
- 20 cm
- 50 cm
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The Correct Option is A
Solution and Explanation
Concept:
Under the assumption of uniform motion, speed is given by:
\[
v=\frac{\text{distance}}{\text{time}}
\]
When Noah reaches the finish line, Kishane is still running. The distance separating them can be calculated from Kishane's speed and the remaining time required for him to complete the race.
Step 1: Calculate the speed of Kishane Thompson. The race length is: \[ 100\,\text{m} \] Time taken by Kishane: \[ t_K=9.789\,\text{s} \] Therefore, \[ v_K=\frac{100}{9.789} \] \[ v_K\approx 10.2155\,\text{m s}^{-1} \]
Step 2: Calculate the time difference between the two athletes. Noah's finishing time: \[ t_N=9.784\,\text{s} \] Kishane's finishing time: \[ t_K=9.789\,\text{s} \] Difference: \[ \Delta t=t_K-t_N \] \[ \Delta t=9.789-9.784 \] \[ \Delta t=0.005\,\text{s} \] Thus, when Noah crosses the finish line, Kishane still requires \(0.005\) s to finish.
Step 3: Determine the remaining distance for Kishane. Distance covered by Kishane in \(0.005\) s: \[ d=v_K\Delta t \] \[ d=(10.2155)(0.005) \] \[ d=0.0511\,\text{m} \] Converting into centimetres: \[ d=0.0511\times100 \] \[ d=5.11\,\text{cm} \]
Step 4: Select the nearest option. \[ d\approx5\,\text{cm} \] Hence the distance between the runners is approximately \(5\) cm. \[ \boxed{\text{Distance} \approx 5\,\text{cm}} \] Therefore, option (A) is correct.
Step 1: Calculate the speed of Kishane Thompson. The race length is: \[ 100\,\text{m} \] Time taken by Kishane: \[ t_K=9.789\,\text{s} \] Therefore, \[ v_K=\frac{100}{9.789} \] \[ v_K\approx 10.2155\,\text{m s}^{-1} \]
Step 2: Calculate the time difference between the two athletes. Noah's finishing time: \[ t_N=9.784\,\text{s} \] Kishane's finishing time: \[ t_K=9.789\,\text{s} \] Difference: \[ \Delta t=t_K-t_N \] \[ \Delta t=9.789-9.784 \] \[ \Delta t=0.005\,\text{s} \] Thus, when Noah crosses the finish line, Kishane still requires \(0.005\) s to finish.
Step 3: Determine the remaining distance for Kishane. Distance covered by Kishane in \(0.005\) s: \[ d=v_K\Delta t \] \[ d=(10.2155)(0.005) \] \[ d=0.0511\,\text{m} \] Converting into centimetres: \[ d=0.0511\times100 \] \[ d=5.11\,\text{cm} \]
Step 4: Select the nearest option. \[ d\approx5\,\text{cm} \] Hence the distance between the runners is approximately \(5\) cm. \[ \boxed{\text{Distance} \approx 5\,\text{cm}} \] Therefore, option (A) is correct.
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