Question

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?

Answer 1

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?

Answer 2

right

Answer 3

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

Answer 4

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

Answer 5

i thought youd have to use the equation dT/dt=DT/Dt=-U*gradientT

Answer 6

I'm still a little confused about the question here, though...

Answer 7

im assuming its temperature advection

Answer 8

what's the context of this question (what class)?

Answer 9

calc 3

Answer 10

and its discusing dynamics

Answer 11

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...

Answer 12

its ok thanks for trying though!