In 1 km races, runner 1 on track 1 (with time 2 min, 28.13 s) appears to be faster than runner 2 on track 2 (2 min, 28.48 s). however, the length l2 of track 2 might be slightly greater than the length l1 of track 1. how large can l2 - l1 be for us still to conclude that runner 1 is faster?

Question

Rosa Stout

Physics

10 June, 08:44

In 1 km races, runner 1 on track 1 (with time 2 min, 28.13 s) appears to be faster than runner 2 on track 2 (2 min, 28.48 s). however, the length l2 of track 2 might be slightly greater than the length l1 of track 1. how large can l2 - l1 be for us still to conclude that runner 1 is faster?

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Liberty · Answer 1

We are given with a velocity-distance-time kinematic problem given the different times of two runners and is asked for the difference in distances the runner has ran in the track. we use the formula v = d/t where d is the distance of running, t is time and v is the velocity of the runner.

First runner,

v = d/t = 1000 m / (120+28.13s) = 6.750826976 m/s

Second runner

Using the same velocity we determine d2.

v = d2/t2 = d2 / (120+28.48s) = 6.750826976 m/s; d2 = 1002.362789

distance of running track is the difference of the two distance achieved by the runners, delta d = d2 - d = 2.362789 m