How Many Meters Did You Win the Race By?

AI Thread Summary
In a discussion about determining the distance won in a 100m dash, a runner's time of 11.800 seconds is compared to a competitor who finished just 0.001 seconds later. The first method calculates the distance won as 0.008 meters using average velocity. However, an alternative method yields a result of 0.00084745 meters, leading to confusion about the discrepancy. The issue arises from a miscalculation in the second method, where the time for the second runner should be adjusted to 11.801 seconds for accurate results. Clarification is sought on the reasons for the differing outcomes.
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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