Calculate Distance Traveled by Jetliner in 35 ms

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Discussion Overview

The discussion revolves around calculating the distance traveled by a commercial jetliner in 35 milliseconds, focusing on the application of significant figures in the context of the calculation. Participants explore differing interpretations of significant figures and precision in measurements.

Discussion Character

  • Technical explanation, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant presents a calculation for the distance traveled by a jetliner, arriving at approximately 10 meters, and questions the textbook's use of significant figures.
  • Another participant suggests that the numbers provided could be considered exact, implying that the precision of the data affects how the answer should be expressed.
  • A third participant agrees with the initial claim that the textbook's answer violates the rules of significant figures, advocating for a rounded answer of "10. meters."
  • Another viewpoint emphasizes that significant figures may not always be the best measure of accuracy, proposing that the answer should reflect the uncertainty in the time measurement instead.
  • One participant asserts that the textbook's answer is incorrect and supports the calculation provided by the first participant as preferable.
  • A later reply introduces the idea that the problem is hypothetical and suggests that the 35 milliseconds should be treated as an exact value, which could influence how partial credit might be awarded.
  • There is uncertainty expressed regarding the educational context, with a participant questioning whether significant figures were emphasized in earlier physics classes.

Areas of Agreement / Disagreement

Participants generally disagree on the application of significant figures and the interpretation of the precision of the given values. Multiple competing views remain regarding how to handle the calculation and the significance of the results.

Contextual Notes

There is a lack of clarity on the precision of the given data, and the discussion reflects differing opinions on the appropriateness of significant figures versus expressing uncertainty in measurements.

DocZaius
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Hi,

I am using a textbook which asks: How far does a commercial jetliner (1046 kilometers/hour) go in 35 milliseconds?

The reason this isn't in the homework section is because I answered this correctly, but apparently not using the book's version of how to handle significant numbers. Maybe you can help me.

here are the calculations I did
1046 kilometers/hour * (1000 meter/1 km) * (1 hr/3600000 ms) * (35 milliseconds)
or
1046 * 1000 / 3600000 * 35 = 10.169444444444444444444444444444 -> rounded to 10 meters since 35 has 2 significant figures and the answer should have no more significant figures in a multiplication/division operation than the number with the least significant figures in it.

The answer given in the textbook is 10.2 (3 significant figures!). Why is the textbook giving 3 significant figures to the answer when a number in the multiplication/division operation clearly has no more than 3 significant numbers in it, but rather has 2. Everywhere I look, this seems to break the rule. I am told everywhere that the answer must not be more than the number in the operation with the least significant figures.
 
Last edited:
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The numbers given as data, could in fact be exact, couldn't they? And what happens if I write 35ms = 35000 microseconds ?
In this case, you have not been told the precsion of the data so it's up to you how you express the answer.
 
I agree that the answer in the book broke the rule. It should be "10. meters"

To leave the final answer on a paper, I would first show too many digits and then show the act of rounding it:

x = (1046 km/hr)(1000 m/1 km)(1 hr/3600000 ms)(35 ms) = 10.16944444 m = 10. m (rounded for 2 significant digits)
 
The other way to look at it. You know the time to +/- 0.5ms or about 3% so you quote your answer to around 3% ie nearest 0.3m

Significant figures aren't necessarily the best approach, ie '10' is accurate to 10% but '98' is accurate to nearely 1% even though both have 2sig fig.
 
The book answer is (strictly) incorrect, and your answer is preferred- mikelepore's response is the ideal one.
 
[edit] Since it is a hypothetical problem, I don't think it is saying the 35 miliseconds is a measurement. It is asking you how far it would go in exactly 35 ms.

I'd ask for partial credit (if available) based on that logic.

Is this a high school physics class? I don't recall if in my elementary physics classes we bothered with sig figs. I'm not sure we did.
 
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