Marathon runner velocity problem

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Homework Help Overview

The discussion revolves around calculating the average velocity required for a marathon runner to meet a qualifying time of 3 hours and 15 minutes for a distance of 42.195 kilometers. The subject area pertains to kinematics and unit conversion.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula for average speed and the necessary unit conversions from kilometers to meters and hours to seconds. Questions arise regarding the correctness of unit cancellation and the resulting calculations.

Discussion Status

Some participants have offered guidance on unit conversion and cancellation, while others are exploring the implications of these conversions on the final calculation. There is an acknowledgment of a mistake in the initial computation, leading to a clarification of the correct average velocity.

Contextual Notes

Participants are working within the constraints of a homework problem that requires precise unit conversions and calculations to determine average velocity. There is an emphasis on understanding the reasoning behind each step rather than simply arriving at a solution.

Allura
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1. Consider a marathon of 42.195 kilometers. In order to attain the qualifying time of 3 hours and 15 minutes to enter the race, a runner would need to run at an average velocity (in m/s) of



2. I thought this would be average speed = distance traveled/time interval spent traveling



3. Since they wanted it in terms of m/s, I divided 42.195 by 1000. Then to get seconds, I converted 3 hr and 15 mins to 11700 seconds, which gives 3.6E-6.

But apparently its wrong. Help?
 
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Why did you divide by 1000?
 


To go from kilometers to meters
 


You are not canceling units correctly:

1 km * 1000 \frac{m}{km} = 1000 m
 


Ohhh, the right is answer is 3.6 then. Thanks! That makes more sense.
 

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