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.