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The air temperature in the atmosphere decreases at the rate of 90C every 300 meters. What height

would an airplane have to fly to experience a temperature of – 810C? The temperature is 00C at sea
level.

User Jabalazs
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1 Answer

3 votes

Answer: To find the height at which the airplane would experience a temperature of -8°C, we can use the given rate of temperature change and the initial temperature at sea level.

Let's assume:

h = height above sea level (in meters)

T = temperature at height h (in °C)

We are given that the temperature decreases at a rate of 9°C every 300 meters. This means the temperature change per meter (dT/dh) is:

dT/dh = -9°C / 300 meters = -0.03°C/meter

The initial temperature at sea level (h = 0 meters) is 0°C.

Now, we can set up a differential equation to relate the temperature T and the height h:

dT/dh = -0.03°C/meter

Next, we can integrate this differential equation to find the relationship between T and h:

∫dT = ∫(-0.03dh)

Integrating, we get:

T = -0.03h + C

where C is the constant of integration.

Now, we can use the initial condition that the temperature is 0°C at sea level (h = 0 meters):

0 = -0.03(0) + C

C = 0

Now, the equation becomes:

T = -0.03h

We want to find the height h at which the temperature T is -8°C:

-8 = -0.03h

Solving for h:

h = -8 / (-0.03)

h = 266.67 meters

Therefore, the airplane would have to fly at a height of approximately 266.67 meters to experience a temperature of -8°C.

User Tylerjw
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