Final answer:
The airplane's speed relative to the air mass is found by subtracting the wind speed from the airplane's speed relative to the Earth.
Step-by-step explanation:
The airplane's speed relative to the air mass can be found using the concept of vector addition. Consider the airplane's speed relative to the Earth as VPE and the wind speed as VW. The airplane's speed relative to the air mass can be determined by subtracting the wind speed from the airplane's speed relative to the Earth, as VPA = VPE - VW.
To find the airplane's speed relative to the air mass, we need to find the vector components of the airplane's speed relative to the Earth and the wind speed. Let's assume that the airplane's speed relative to the Earth is 200 km/h and the wind speed is 50 km/h blowing directly out of the west. The x-component of the airplane's speed relative to the Earth is 200 km/h and the y-component is 0 km/h. The x-component of the wind speed is -50 km/h and the y-component is 0 km/h.
Using vector addition, the x-component of the airplane's speed relative to the air mass is the sum of the x-components of the airplane's speed relative to the Earth and the wind speed, which is 200 km/h + (-50 km/h) = 150 km/h. The y-component remains 0 km/h. Therefore, the airplane's speed relative to the air mass is 150 km/h.
Therefore, the correct answer is (a) 150 km/h.