How Many Meters Did You Win the Race By?

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SUMMARY

The discussion centers on calculating the distance by which a runner wins a 100.000 m race, given a total time of 11.800 seconds and a margin of victory of 0.001 seconds. The correct calculation shows that the winner wins by 0.008 meters using the formula v = x/t, where v is average velocity. However, an alternative method yields a different result of 0.00084745 meters, leading to confusion regarding the discrepancy. The issue arises from the precision of the average velocities calculated for both the winner and the loser.

PREREQUISITES
  • Understanding of basic physics concepts such as average velocity (v = x/t)
  • Familiarity with unit conversions in metric measurements
  • Ability to perform calculations involving time and distance
  • Knowledge of significant figures and precision in measurements
NEXT STEPS
  • Review the concept of average velocity and its calculation in physics.
  • Learn about significant figures and how they affect precision in calculations.
  • Explore the implications of rounding errors in mathematical computations.
  • Investigate the differences in results when using varying levels of precision in measurements.
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Students studying physics, athletes analyzing race performance, and anyone interested in understanding the impact of precision in calculations.

jesusu2
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Homework Statement


You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?

Homework Equations


vavg=Δx/Δt
v=x/t

The Attempt at a Solution


I have the answer already with the method for solving it:
v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!
 
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jesusu2 said:

Homework Statement


You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?



Homework Equations


vavg=Δx/Δt
v=x/t

The Attempt at a Solution


I have the answer already with the method for solving it:
v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!

The two values in red do not match. Second should be 11.801
 

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