Vector Addition Using Components

[Turquoise]

Homework Statement

Two forces are acting on a mass. One of the forces is a 40.0 N force and the other force is 30.0 N at the angles shown below:

The magnitude of the force is:
a) 15.3 N
b) 15.6 N <-- correct answer
c) 46.6 N
d) 69.0 N

Homework Equations

Pythagorean Therom
Cosine, Sine

The Attempt at a Solution

Vector

X component

A ax = (30.0N) Cos 20.0 = 28.2 N
B bx = (40.0 N)Cos 40.0 N = 30.6 N

Y component
ay = (30.0N)Sin 20.0 = 10.3 N
by = (40.0 N) Sin 40.0N = 25.7 N

C = ax+bx = 58.8 N Cy = 36 N

C = cx^2 + cy^2
C = 58.8N^2 + 36 N^2
C = 69 N

I keep getting 69 N and its not the correct answer. The correct answer is 15.6. I'm following the directions from my notes, but it gives me 69 every time. Help! What am I doing wrong?

 

[Carid]

Vectors have magnitude and direction.

Your ax and by are pulling in opposite directions, so are ay and by.

So subtraction, not addition, is the order of the day.

Then the magnitude of the resultant vector C will be the square root of the sum of the squares of the x and y components

 

[Turquoise]

Thanks! I got the correct answer now ;)