Adding vectors with the component method

[personguything]

Hi! I know this is pretty basic... I'm teaching myself from a textbook, and I got a different answer from the book...It doesn't have the problem worked out, just the answer. I just need to figure out what mistake I made.

Homework Statement

Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

2. The attempt at a solution
First I name each vector
30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

Next I find the x and y components for each vector
a_x = 30*cos(40) = 23;
a_y = 30*sin(40)
---
b_x = 120*cos(35) = 98.3;
b_y = 120*sin(35) = 68.8
---
c_x = 60*sin(260) = -59.1;
c_y = 60*cos(260) = -10.4
---
Next I find the x and y components of the resultant vector
R_x = a_x+b_x+c_x = 62.2
R_y = a_y+b_y+c_y = 62.2

Next I find the hypotenuse(i.e. the magnitude of the resultant vector)
R = √((62.2)^2+(77.7)^2) = 99.5

And finally I calculate the angle of the resultant vector
θ = arctan(77.7/62.2) = 51.3

 

[gneill]

Hi! I know this is pretty basic... I'm teaching myself from a textbook, and I got a different answer from the book...It doesn't have the problem worked out, just the answer. I just need to figure out what mistake I made.

Homework Statement

Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

2. The attempt at a solution
First I name each vector
30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

Next I find the x and y components for each vector
a_x = 30*cos(40) = 23;
a_y = 30*sin(40)
---
b_x = 120*cos(35) = 98.3; <---- Isn't the angle 135° ?
b_y = 120*sin(35) = 68.8
---
c_x = 60*sin(260) = -59.1; <---- Looks like you've swapped sin and cos
c_y = 60*cos(260) = -10.4
---
Next I find the x and y components of the resultant vector
R_x = a_x+b_x+c_x = 62.2
R_y = a_y+b_y+c_y = 62.2

Next I find the hypotenuse(i.e. the magnitude of the resultant vector)
R = √((62.2)^2+(77.7)^2) = 99.5

And finally I calculate the angle of the resultant vector
θ = arctan(77.7/62.2) = 51.3

Redo you calculations after fixing up the bits I've indicated. Be careful about the quadrant placement for the angle.

 

[personguything]

Redo you calculations after fixing up the bits I've indicated. Be careful about the quadrant placement for the angle.

Thank you! I 100% missed the "35" mistake haha. The cos/sin switch was on purpose, something about it being below the x-axis...Anyway, I worked through it all visually and mathematically and figured it out.

I appreciate it!