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ranyai12

  • 3 years ago

A Michigan student is driving southeastward (passing Ann Arbor) at a speed of 45 miles/h and measures a temperature rise of 1 K/h. In addition, we observe that the air at a point 80 miles west-north-west (WNW) of Ann Arbor is 4 °C colder than in Ann Arbor. Assume that the temperature varies linearly in the WNW direction. What is the local temperature change in Ann Arbor?

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  1. whpalmer4
    • 3 years ago
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    Okay, so the driver is going 45 miles every hour. The temperature rises 1 K/h, so every 45 miles, it rises 1 K, right?

  2. ranyai12
    • 3 years ago
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    right

  3. whpalmer4
    • 3 years ago
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    we can think of this as a line where the slope is 1K/45 miles, the x-value is the distance from that spot 80 miles WNW of Ann Arbor

  4. whpalmer4
    • 3 years ago
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    in fact, the assumption that the temperature varies linearly invites that very thought, because any linear equation can be written as y = mx + b, by definition, really

  5. ranyai12
    • 3 years ago
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    i thought youd have to use the equation dT/dt=DT/Dt=-U*gradientT

  6. whpalmer4
    • 3 years ago
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    I'm still a little confused about the question here, though...

  7. ranyai12
    • 3 years ago
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    im assuming its temperature advection

  8. whpalmer4
    • 3 years ago
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    what's the context of this question (what class)?

  9. ranyai12
    • 3 years ago
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    calc 3

  10. ranyai12
    • 3 years ago
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    and its discusing dynamics

  11. whpalmer4
    • 3 years ago
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    hmm...I think I'm going to have to bow out, I'm not confident at this point that I understand the question. sorry! at first it looked like this was just a simple application of slope of a line problem...

  12. ranyai12
    • 3 years ago
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    its ok thanks for trying though!

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