As dry air moves upward, it expands and in so doing cools at a rate of about 10C for 100m rise, up to about 12 km.
a) If the ground temperature is 220, write a formula for the temperature at height x km.
Answer:
b) What range of temperature can be expected if a plane takes off and reaches a maximum height of 9 km.Write answer in interval notation.
Answer:
a) To find the formula for the temperature at a height x km, we need to know the initial temperature and the rate at which the temperature decreases with height. Given that the ground temperature is 220°C and the rate of cooling is 10°C for every 100m rise, we can determine the formula as follows:
1 km = 1000 m
100 m = 1°C cooling
∴ 1 km = 10°C cooling
So, for every 1 km rise, the temperature decreases by 10°C. Therefore, the formula for the temperature at height x km is:
Temperature = Initial Temperature - 10x
b) If the maximum height reached by the plane is 9 km, we can find the range of temperature by substituting the value of x into the formula derived in part (a):
Temperature = 220 - 10(9)
Temperature = 220 - 90
Temperature = 130°C
Therefore, the range of temperature that can be expected when the plane reaches a maximum height of 9 km is:
(130°C, 130°C] (since the temperature decreases with height, the minimum and maximum temperatures are the same)