Vector application

Question

An airplane is traveling at a fixed altitude with a negligible wind factor. The airplane is headed N30W at a speed of 500 miles per hour. As the airplane reaches a certain point, it encounters a wind with a velocity of 70 mph in the direction of N45E. What are the resultant speed and bearing of the airplane?

Answer 1

Hi,

given the speed of the plane, Vp and speed of wind Vw we can calculate the resulting speed of plane Vr and its bearing.

1. we want to get the Vr by its components (x and y) So Vxr=Vxp-Vxw and Vyr=Vyp-Vyw
2. we want to calculate Vr=square root of (Vxr² + Vyr²)
3. we want the bearing= arctan(Vyr/Vxr)

Plugging in the numbers we will get:

1. Vxr=500cos(30) -70cos(45)= 383.38 and Vyr=500sin(30)-70cos(45)= 200.35
2. Vr=square root of (383.38)²+(200.35)² =432.58mph
3. arctan(200.35/383.38)=27.59 degrees NW

Thus the planes speed will be 432.58 mph with a bearing of N27.6W