Solve Homework: Determine Max L2-L1 for Runner 1 to be Faster

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SUMMARY

The discussion centers on determining the maximum difference in lengths (L2 - L1) between two tracks for runner 1 to still be considered faster than runner 2 in a 1 km race. Given runner 1's time (t1 = 147.95 s) and runner 2's time (t2 = 148.15 s), the inequality L2t1 - L1t2 < 0 is established. By substituting L1 with 1 km, the problem simplifies, allowing for a clear calculation of the maximum permissible difference in track lengths.

PREREQUISITES
  • Understanding of basic physics concepts, specifically velocity (v = L / t)
  • Familiarity with algebraic manipulation of inequalities
  • Knowledge of unit conversions, particularly kilometers to meters
  • Basic comprehension of race timing and performance metrics
NEXT STEPS
  • Calculate the maximum difference L2 - L1 using the established inequality
  • Explore the implications of track length variations on race outcomes
  • Review concepts of average speed and its calculation in competitive sports
  • Investigate how timing discrepancies affect performance analysis in athletics
USEFUL FOR

Students studying physics or mathematics, coaches analyzing race performance, and athletes seeking to understand the impact of track conditions on race outcomes.

GunnaSix
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Homework Statement


In 1 km races, runner 1 on track 1 (with time t1 = 147.95 s) appears to be faster than runner 2 on track 2 (t2 = 148.15 s). However, length L2 of track 2 might be slightly greater than length L1 of track 1. How large can L2 - L1 be for us to still conclude that runner 1 is faster?


Homework Equations


v = L / t


The Attempt at a Solution


I got it down to L2t1 - L1t2 < 0, but can't figure out how to get L2 - L1 out. I know I probably have to use the fact that L is approximately 1 km, but I'm not seeing how to do it.
 
Physics news on Phys.org
Hi GunnaSix! :smile:

Why not just put L1 = 1 km?
 

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