(a) As dry air moves upward, it expands and cools. If the ground temperature is 30°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent? (c) What is the temperature at a height of 1.5 km? Solution (a) Because we are assuming that Tis a linear function of h, we can write T= mh + b. We are given that T = 30 when h = 0, so 30 = m· + b In other words, the y-intercept is b = 30 We are also given that T = 10 when h = 1, so 1 v ) + (30 10 = m. The slope of the line is therefore m = 10 – and the required linear function is T = (b) The graph is sketched in the figure below. 20 3 4 -20 - 40 The slope ism = °C/km, and this represents the rate of change of ---Select--- v with respect to ---Select--- v (c) At a height of h = 1.5 km, the temperature is

(a) As dry air moves upward, it expands and cools. If the ground temperature is 30°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent? (c) What is the temperature at a height of 1.5 km? Solution (a) Because we are assuming that Tis a linear function of h, we can write T= mh + b. We are given that T = 30 when h = 0, so 30 = m· + b In other words, the y-intercept is b = 30 We are also given that T = 10 when h = 1, so 1 v ) + (30 10 = m. The slope of the line is therefore m = 10 – and the required linear function is T = (b) The graph is sketched in the figure below. 20 3 4 -20 - 40 The slope ism = °C/km, and this represents the rate of change of ---Select--- v with respect to ---Select--- v (c) At a height of h = 1.5 km, the temperature is

Name: (a) As dry air moves upward, it expands and cools. If the ground temp
Uploaded: 2024-03-20T07:06:41.000Z
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Description: (a) As dry air moves upward, it expands and cools. If the ground temperature is 30°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is ap