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Question 1208335: The dynamic pressure (P) on the wall increased with the square of the speed (s). Initially, P =s = 0. At a speed of 30, the pressure was 13.5. Which of the following functions represents pressure as a function of airspeed? A) P(s)=√6s B) P(s) = 0.015s2 C) P(s) = 1.15 D) P(s) = 0.45s
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060)   (Show Source):
Answer by ikleyn(52816)  (Show Source):
You can put this solution on YOUR website! .
The dynamic pressure (P) on the wall increased with the square of the speed (s).
Initially, P =s = 0. At a speed of 30, the pressure was 13.5.
Which of the following functions represents pressure as a function of airspeed?
A) P(s)=√6s B) P(s) = 0.015s2 C) P(s) = 1.15 D) P(s) = 0.45s
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Of the four given optional functions (A), (B), (C) and (D), only function (B)
increases with the square of the speed.
We only should to check, if this function has the assigned values
P(0) = 0 and P(30) = 13.5.
So, we substtute s= 0 into function (B), and we get P(0) = 0.015*0^2 = 0,
which corresponds to the given value.
Next, we substtute s= 30 into function (B), and we get P(30) = 0.015*30^2 = 13.5,
which corresponds to the given value, too.
Thus function (B) satisfies all imposed conditions.
So, (B) is the ANSWER.
Solved.
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The thing which embarrasses me in this problem is the fact that in the "given" part
they talk about "speed", while the question asks about "airspeed".
In true Math problem, all used conceptions must be consistent and do not to raise questions.
Therefore, in this problem, I would replace the term "speed" by the "air speed",
and the term "airspeed" by the term "air speed", too, in order for everything
be clear and do not to confuse the reader.
By the way, the term "airspeed" is not what you think.
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By the definition, "airspeed" is "the speed of an aircraft relative to the air through which it is moving."
It is not "air speed", as you may think.
The term "airspeed" has one and only one meaning, totally different from the meaning of "air speed".
One goal of Math problems (the major goal) is to teach young students to think
and to solve Math problems correctly.
The other, auxiliary goal, is to teach young students to new conceptions and to new terminology
by introducing new conceptions carefully and using relevant terminology adequately.
So, the auxiliary goal is to teach students to speak correctly, in addition to think correctly.
As this problem is worded and printed in the post, it failed this auxiliary goal TOTALLY.
As the problem is worded in the post, it makes clear, that the composer/writer
does not know the subject and does not know terminology.
It is sad to see it.
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