Question

Find the magnitude of the resultant force and the angle that makes with the positive x-axis

Answer 1

\(F1=75 N; θ=0\)
\(F2=50 N; θ=30\)
\(F3=40 N; θ=150\)

F1=
\(f_1x=75cos(0)=75 N\)
\(f_1y=75sin(0)=0 N\)

F2=
\(f_2x=50cos(30)=25\sqrt{3} N\)
\(f_2y=50sin(30)=25 N\)

F3=
\(f_3x=40cos(150)=−20\sqrt{2}N\)
\(f_3y=40sin(150)=20 N\)

Answer 2

Is this good so far?

Answer 3

I don't agree with f3x

Answer 4

everything else looks good

Answer 5

Looks good! next simply add them component by component

Answer 6

Ahh I didn't check the arithmetic..

Answer 7

this should fix it :

\(F1=75 N; θ=0\)
\(F2=50 N; θ=30\)
\(F3=40 N; θ=150\)

F1=
\(f_1x=75cos(0)=75 N\)
\(f_1y=75sin(0)=0 N\)

F2=
\(f_2x=50cos(30)=25\sqrt{3} N\)
\(f_2y=50sin(30)=25 N\)

F3=
\(f_3x=40cos(150)=−20\sqrt{\color{red}{3}}N\)
\(f_3y=40sin(150)=20 N\)

Answer 8

much better

Answer 9

Okay. Thanks! @jim_thompson5910 and @ganeshie8 !!!
I'll deal with the arithmetic, it's not the problem for me now. But the next step is what i'm having problems with.

Answer 10

you have the vector components, add up the corresponding components

Answer 11

u = <a,b>
v = <c,d>
w = <e,f>

u+v+w = <a+c+e, b+d+f>