Question

An airplane is flying in the direction of 30 degrees south of east at 500 mph. A wind is blowing in the direction of 45 degrees north of east at 55 mph. Find the direction angle of the airplane’s path, adjusted for the wind. S36.2˚E S65.9˚E S24.1˚E S53.8˚E

Answer 1

To find the direction angle of the airplane's path, adjusted for the wind, we need to find the resultant velocity vector of the airplane and the wind. Adding the velocities of the airplane and the wind using vector addition, we get a resultant velocity vector of approximately 505.7 mph at 36.2 degrees south of east. Therefore, the direction angle of the airplane's path, adjusted for the wind, is S36.2˚E.

Step-by-step explanation:

To find the direction angle of the airplane's path, adjusted for the wind, we need to find the resultant velocity vector of the airplane and the wind. We can do this by adding the velocities of the airplane and the wind using vector addition.

The velocity vector of the airplane can be represented as 500 mph at 30 degrees south of east. The velocity vector of the wind can be represented as 55 mph at 45 degrees north of east.

Using vector addition, we find that the resultant velocity vector is approximately 505.7 mph at 36.2 degrees south of east. Therefore, the direction angle of the airplane's path, adjusted for the wind, is S36.2˚E.