Question

which of the following scenarios is possible for the resultant velocity of an airplane in a strong wind to be 50 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 200 m/s. the airplane is flying with the wind at 50 m/s. c the wind is blowing at 50 m/s. the airplane is flying against the wind at 100 m/s. d the wind is blowing at 10 m/s. the airplane is flying against the wind at 140 m/s.

Explanation:

Step1: Recall resultant - 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

$v = v_{plane}+v_{wind}=130 + 20=150$ m/s.

Step3: Analyze option B

$v = v_{plane}+v_{wind}=50 + 200 = 250$ m/s.

Step4: Analyze option C

$v=|v_{plane}-v_{wind}|=|100 - 50|=50$ m/s.

Step5: Analyze option D

$v=|v_{plane}-v_{wind}|=|140 - 10| = 130$ m/s.

Answer:

C. The wind is blowing at 50 m/s. The airplane is flying against the wind at 100 m/s.