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In a test I took recently in my beginning Physics class there was a question that really irked me:

A man is swimming upstream at 10 mph. The water is flowing downstream at 5 mph.

How fast is the man moving?

Well, you can actually take this question two ways:

  1. Firstly, "a man is swimming upstream at 10 mph" could mean exactly what it sounds like, and therefore the 5 mph down-streaming water is irrelevant and the man was actually using enough force to swim 15 mph in stationary water. That means he was moving at a speed of 10 mph, like it stated.

  2. Alternatively, it could be taken to mean "a man is swimming upstream at 10 mph", meaning that that is the amount of force he is using. The man is using enough force to swim 10 mph in stationary water. Then, if the water is moving downstream at 5 mph, then he is moving at a speed of 5 mph.

I chose the first answer, but I want to figure out if I got the question right. Is there a way to tell? As in some sort of order of operation for Physics?

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The world record for the 50m freestyle is 20.91s for an average speed of 5.3 mph. Swimming at 10mph is far-fetched no matter how you slice it. –  Mark Eichenlaub May 4 '11 at 4:36
    
@Mark: Best answer, make it so! –  Raskolnikov May 5 '11 at 8:29
    
@Mark :You are right and wrong. "The world record for the 50m freestyle is 20.91s" is also irreal because those values are unattainable (inaccurate at least: $50m\pm XTolerance$ is $20.91s\pm YTolerance$). Any measure is only an approximation. The concretization of a precise value, from within a continuum domain, is unachievable. –  Helder Velez May 5 '11 at 10:50
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3 Answers

up vote 1 down vote accepted

David answer is ok. A man is swimming upstream at 10 mph -- is undefined : in relation to the ground or in relation to the water?, probably in relation to the ground

water is flowing downstream at 5 mph. -- probably in relation to the ground

How fast is the man moving? -- is undefined : in relation to the ground or in relation to the water? probably in relation to the ground

motion begs in relation to

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great point, I never thought of it that way –  Matthew May 4 '11 at 2:31
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Nope. The question is ambiguous.

In any case, if there is a way to resolve this ambiguity, it's a question of language interpretation. The physics only really starts once you've figured out what the question means. (To be fair, it's often the case that most of the difficulty in doing a physics problem is just translating it from English into math :-P)

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thanks! I guess I'll just have to wait and see how my teacher grades it –  Matthew May 4 '11 at 2:05
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If this is only a simple High School Test, then they probably wouldn't be going in so deep as to whether the man was moving in relation as to what. All they would want is probably the man's moving speed after being slowed down by the flow of the stream

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good point, but the trouble of Matthew with "you can actually take this question two ways" is showing that he is concerned with the 'Relativity of motion', as stated in the title of the Question (not the relativistic speeds but nevertheless a relativity question). –  Helder Velez May 5 '11 at 10:37
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