Question

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

Answer 1

Answer:

B. The wind is blowing at 20 m/s. The airplane is flying with the wind at 130 m/s.

Explanation:

From Physics we get that resultant velocity of an airplane is the sum of an absolute velocity and a relative velocity, that is:

$\vec v_{A} = \vec v_{W}+\vec v_{A/W}$ (Eq. 1)

Where:

$\vec v_{W}$ - Wind velocity, measured in meters per second.

$\vec v_{A/W}$ - Airplance velocity relative to wind, measured in meters per second.

$\vec v_{A}$ - Airplane velocity, measured in meters per second.

If we assume that $\vec v_{W} = 20\,\hat{i}\,\,\,\left[\frac{m}{s} \right]$ (The airplane flies with the wind), $\vec v_{A/W} = 130\,\hat{i}\,\,\,\left[\frac{m}{s} \right]$, then the resultant velocity of the airplane is:

$\vec v_{A} = 20\,\hat{i}+130\,\hat{i}\,\,\,\left[\frac{m}{s} \right]$

$\vec v_{A} = 150\,\hat{i}\,\,\,\left[\frac{m}{s} \right]$

Therefore, correct answer is B.