Vector Components Question

  • #1
What are the resultant components of the vectors?

Homework Statement



Determine the sum of the following three vectors. Give the resultant in terms of a. components, b. magnitude and angle with x-axis.

Vector A has a magnitude of 66 at an angle of 28 degrees northeast (quadrant 1)
Vector B has a magnitude of 40 at an angle of 56 degrees northwest (quadrant 2)
Vector C has a magnitude of 46.8 at an angle of 0 (on y-axis between Quadrant 3 and 4)

Homework Equations



Vx = Dcos0
Vy = Dsin0
Vx = V1x+V2x+V3x
Vy = V1y+V2y+V3y
Vy/Vx = tan θ


The Attempt at a Solution



So here is how I started

A: Vx = +(66)(cos 28) = 58.27454
Vy = +(66) (sin 28) = 30.985

B: Vx = -(40)(cos 56) = -22.3677
Vy = +(40)(sin 56) = 33.1615

C: Vx = (46.8)(cos 0) = 46.8
Vy = (46.8) (sin 0) = 0

Then I would add the three parts of Vx to get overall Vx (58.27454-22.3677+46.8) = 82.70684 & the three parts of Vy to get overall Vy (30.085+33.1615+0) = 63.2467.

This means the components would be (82.70684, 63.2467) and I would continue with pythagorean theorem to get the magnitude & use the arctan formula to get the angle. However, my answer for components is incorrect, the book says it should be (35.9,17.3). What did I do wrong? Thank you so much in advance.
 
Last edited:

Answers and Replies

  • #2
1,198
5
Your computation for vector C is wrong. I get their answer. How can it have an x component when it lies on the y axis?
 

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