Vectors componenets relative motion help

[P944]

Homework Statement

Hello. I was wondering if you guys could help me tell me why i am getting this problem wrong.

Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 12.1 m/s due north. Plane 2 taxies with a speed of 6.3 m/s in a direction 21.2° north of west.
(a) What are the direction and magnitude of the velocity of plane 1 relative to plane 2?
Direction _______° north of east
Magnitude ________m/s

(b) What are the direction and magnitude of the velocity of plane 2 relative to plane 1?
Direction ______° south of west
Magnitude ________ m/s

Homework Equations

The Attempt at a Solution

I First drew out a parallelogram with the magnitude and direction of plane 1 then drew plane 2's tail to the head of plane 1 to visualize the problem. Next i used components of a vector to solve for the magnitude and direction.

plane 1 -> x = 12.1 cos 90 =0
plane 2 -> x = 6.3 cos 21.2 = 5.874

plane 1 -> y = 12.1 sin 90 = 12.1
plane 2 -> y = 6.3 sin 21.2 = 2.278

I added the vectors (5.874 m/s) x + (14.38 m/s) y

To find the magnitude of the resultant i got sq root (5.874 m/s)^2 + (14.38 m/s)^2 = 15.53

theta = inverse tan (14.378/5.8736) = 67.78 degrees

b) I was confused on this one. I thought that from plane 2 the angle would be 67.78 + 180 = 247.8 degrees with the same magnitude of 15.53?

I would greatly appreciate if someone could help me out and let me know what i did wrong. Thanks so much! :)

 

[tiny-tim]

Hi P944!

Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 12.1 m/s due north. Plane 2 taxies with a speed of 6.3 m/s in a direction 21.2° north of west.
(a) What are the direction and magnitude of the velocity of plane 1 relative to plane 2?
…
I First drew out a parallelogram with the magnitude and direction of plane 1 then drew plane 2's tail to the head of plane 1

No, that will add the velocities.

For a relative velocity, you always need to subtract.

If g is "ground", then you want V₁₂, which = V_1g + V_g2 = V_1g - V_2g

(if you draw arrows, this should be obvious)