Question

1. which of the following scenarios is possible for the resultant velocity of an airplane in a strong wind to be 150 m/s?

a. the wind is blowing at 20 m/s. the airplane is flying with the wind at 130 m/s.
b. the wind is blowing at 50 m/s. the airplane is flying against the wind at 100 m/s.
c. the wind is blowing at 10 m/s. the airplane is flying against the wind at 140 m/s.
d. the wind is blowing at 200 m/s. the airplane is flying with the wind at 50 m/s.

Explanation:

Step1: Recall relative - velocity formula

When the airplane is flying with the wind, the resultant velocity $v = v_{plane}+v_{wind}$. When flying against the wind, $v = |v_{plane}-v_{wind}|$.

Step2: Analyze Option A

If the wind is blowing at $20\ m/s$ and the airplane is flying with the wind at $130\ m/s$, then the velocity of the airplane in still - air $v_{plane}=130 - 20=110\ m/s$. The resultant velocity when flying against the wind would be $|110 - 20| = 90\ m/s
eq150\ m/s$.

Step3: Analyze Option B

If the wind is blowing at $50\ m/s$ and the airplane is flying against the wind at $100\ m/s$, then the velocity of the airplane in still - air $v_{plane}=100 + 50 = 150\ m/s$. When flying with the wind, the resultant velocity is $150+50 = 200\ m/s
eq150\ m/s$.

Step4: Analyze Option C

If the wind is blowing at $10\ m/s$ and the airplane is flying against the wind at $140\ m/s$, then the velocity of the airplane in still - air $v_{plane}=140 + 10=150\ m/s$. When flying with the wind, the resultant velocity is $150 + 10=160\ m/s
eq150\ m/s$.

Step5: Analyze Option D

If the wind is blowing at $200\ m/s$ and the airplane is flying with the wind at $50\ m/s$, then the velocity of the airplane in still - air $v_{plane}=50 - 200=- 150\ m/s$ (magnitude $150\ m/s$). When flying against the wind, the resultant velocity is $|150 - 200|=50\ m/s
eq150\ m/s$. But if we consider the magnitudes and the concept of relative velocity correctly, assume the velocity of the airplane in still - air is $v_{plane}$ and the wind velocity is $v_{wind}$. When flying with the wind $v_{with}=v_{plane}+v_{wind}$ and when flying against the wind $v_{against}=|v_{plane}-v_{wind}|$. Let the velocity of the airplane in still - air be $150\ m/s$ and the wind velocity be $0\ m/s$, the resultant velocity is $150\ m/s$. In a more general sense, if we assume the airplane's speed in still - air is $150\ m/s$ and the wind speed is $0\ m/s$ (a special case where the 'strong wind' might be a mis - statement or we consider the limiting case), the resultant velocity of the airplane is $150\ m/s$.

Answer:

All options seem incorrect based on normal relative - velocity calculations. But if we consider the case where the wind speed is $0\ m/s$ (a non - typical interpretation of 'strong wind' but valid in the context of relative velocity being $150\ m/s$ as the airplane's velocity in still - air), there is no correct option among the given ones as presented with the information about wind - airplane motion combinations. If we assume some errors in the problem setup or a very special case, we note that the problem has no straightforward correct answer from the given choices.