Question

use vector diagrams to show magnitude and direction and to show the addition of parallel and perpendicular vectors. activating strategy essential questions warm - up #2 how do i work with vectors graphically? i can... continue to solve vector problems using graphing warm up 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 10 m/s. the airplane is flying against the wind at 140 m/s. b. the wind is blowing at 20 m/s. the airplane is flying with the wind at 130 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 200 m/s. the airplane is flying with the wind at 50 m/s.

Explanation:

Step1: Recall vector - addition formula for velocities

When the airplane is flying with the wind, the resultant velocity $v_r=v_a + v_w$ (where $v_a$ is the airplane's velocity relative to the air and $v_w$ is the wind - velocity). When flying against the wind, $v_r=\vert v_a - v_w\vert$.

Step2: Analyze option a

The wind is blowing at $v_w = 10$ m/s and the airplane is flying against the wind at $v_a=140$ m/s. Then $v_r=\vert140 - 10\vert=130$ m/s.

Step3: Analyze option b

The wind is blowing at $v_w = 20$ m/s and the airplane is flying with the wind at $v_a = 130$ m/s. Then $v_r=130 + 20=150$ m/s.

Step4: Analyze option c

The wind is blowing at $v_w = 50$ m/s and the airplane is flying against the wind at $v_a = 100$ m/s. Then $v_r=\vert100 - 50\vert=50$ m/s.

Step5: Analyze option d

The wind is blowing at $v_w = 200$ m/s and the airplane is flying with the wind at $v_a = 50$ m/s. Then $v_r=200 + 50=250$ m/s.

Answer:

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