Subtracting/multiply vector clarification on worked problem

[rfig08d]

Hello! I've been studying for physics and come across a problem that I've been working on from the textbook. I would just like some clarification as we have not fully covered this subject yet in the class sessions.

Homework Statement

A vector, Avector, has a magnitude of 15 w/ an angle of 25deg with x-axis, vector B has a length of 25 and makes an angle of 70 deg with x-axis. Compute the magnitudes and directions of the vectors: Cvector = Avector + 4*Bvector and Cvector = Avector - Bvector

Homework Equations

Problem 1: Cx = Ax - Bx and Cy = Ay - By

Problem 2: Bx = KAx and By = KAy

The Attempt at a Solution

For the 1st problem:

Ax = 13.6
Bx= 8.6
Ay = 6.3
By = 23.5
Leads to Cx = 5, Cy = -17.2
Size of Cvector = 17.9 from Pythagorean theorem
Angle of cvector = arctan (Cy/Cx) = -73.8

For the 2nd problem:

Bx = KAx = 4(13.6)= 54.4
By = KAy = 4(6.3) = 25.2

Now question here, since I have the multiplied 4B components, do I just treat the rest of the problem as an addition equation? So:

Cx = Ax + Bx and Cy = Ay + By

Cx = 13.6 + 54.4 = 68
Cy = 6.3 + 25.2 = 31.5


thank you for any help :)

 

[kuruman]

Ax = 13.6
Bx= 8.6
Ay = 6.3
By = 23.5
Leads to Cx = 5, Cy = -17.2
Size of Cvector = 17.9 from Pythagorean theorem
Angle of cvector = arctan (Cy/Cx) = -73.8

Looks OK.

For the 2nd problem:

Bx = KAx = 4(13.6)= 54.4
By = KAy = 4(6.3) = 25.2

Why are you using the components of A? If B = (8.6, 23.5), then KB = (K*8.6, K*23.5).

Now question here, since I have the multiplied 4B components, do I just treat the rest of the problem as an addition equation?

Yes you do, but you need to find the correct vector for 4B.

 

[rfig08d]

Oh wow, can't believe I didn't notice that beforehand.

I overlooked it because I was reading the textbook and saw the formula for multiple vectors of Bx = KAx.

Thanks for the help, greatly appreciate it!:)