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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?

Respuesta :

meerkat18
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 

The distance between runner 1 and runner 2 is 2.362m

Data;

  • t1 = 2.0min 28.13s
  • t2 = 2.0min + 28.48s

Conversion of Time from Minutes to Seconds

Let's convert the time to a uniform unit.

[tex]t_1 = 2.0min+28.13s = (2.0*60)+28.13 = 148.13s\\t_2 = 2.0min + 28.48s = (2.0*60) + 28.48 = 148.48s[/tex]

From the above,

  • t1 = 148.13s
  • t2 = 148.48s

Velocity of the athletes

To actually know their speed and know the distance they're apart from each other, we can use a ratio.

[tex]\frac{l_1}{t_1}= \frac{l_2}{t_2}\\[/tex]

solving for L2 - L1

[tex]L_2-L_1=L_1(\frac{t_2}{t_1} - 1)\\L_2 - L_1 = 1000(\frac{148.48}{148.13} -1)\\L_2-L-1 = 1000(1.00236 -1)\\L_2 - L_1 = 1000 * 0.002362\\L_2 - L_1 = 2.362m[/tex]

The distance between runner 1 and runner 2 is calculated as 2.362m

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