Vector subtraction: Plane A is traveling 30.0 degrees west of north at 455 miles/hour

[fisheverlasting]

Hello,
First of all I'm sorry if this is the wrong category. This is for a physics course and I was not sure where to put it, but I believe this is where it should go given the inclusion of vectors.

Second: I have been looking at this problem stumped for an hour. Below, I have included my picture of the problem, as well as four possible resultants (labeled R_1-8).

We were taught (just yesterday) to add vectors via the 'tail to tip' method-- that is, drawing a line from the starting point to the end point. We were also instructed that in order to 'subtract' vectors, we should draw a 'negative' form of the vector being subtracted-- that is, mirror it across both the X and Y axes-- and then 'add' those two. That much makes some degree of sense; what I am confused about here begins with the wording of the problem. If the resultant is plane B relative to plane A, does that mean you START with plane B's 'start point', then add on A's path, then draw a resultant starting where B started and endin where A ends? Or backwards? Or do you start with B and stack on A?

Here is the original problem:
Plane A is traveling 30.0 degrees west of north at 455 miles per hour. Plane B is traveling 22.5 degrees north of east at 344 miles per hour. What is the relative velocity (magnitude and direction) of plane B with respect to plane A? (you do not have to convert to meters/second in this problem.) (Hint: this is a vector subtraction problem.)
My drawing of the problem:

Possible resultants:

 

[HallsofIvy]

Hello,
First of all I'm sorry if this is the wrong category. This is for a physics course and I was not sure where to put it, but I believe this is where it should go given the inclusion of vectors.

Second: I have been looking at this problem stumped for an hour. Below, I have included my picture of the problem, as well as four possible resultants (labeled R_1-8).

We were taught (just yesterday) to add vectors via the 'tail to tip' method-- that is, drawing a line from the starting point to the end point. We were also instructed that in order to 'subtract' vectors, we should draw a 'negative' form of the vector being subtracted-- that is, mirror it across both the X and Y axes-- and then 'add' those two. That much makes some degree of sense; what I am confused about here begins with the wording of the problem. If the resultant is plane B relative to plane A, does that mean you START with plane B's 'start point', then add on A's path, then draw a resultant starting where B started and endin where A ends? Or backwards? Or do you start with B and stack on A?

The problem asks you to find "the relative velocity of plane B with respect to plane A". If A and B were moving in a straight line, A going at 100 mph and B at 150 mph, a person in plane A would see plane B moving away at 150- 100= 50 mph. plane B would be moving at 50 mph "with respect to plane A". So, as the problem says, this is a subtraction problem- you want to subtract plane B's velocity vector from plane A's velocity vector. That is the same as adding -B to A so is vector "\(\displaystyle R_3\)" in your pictures.

Here is the original problem:
Plane A is traveling 30.0 degrees west of north at 455 miles per hour. Plane B is traveling 22.5 degrees north of east at 344 miles per hour. What is the relative velocity (magnitude and direction) of plane B with respect to plane A? (you do not have to convert to meters/second in this problem.) (Hint: this is a vector subtraction problem.)
My drawing of the problem:

Possible resultants: