# Resultant vector relative to x and y axis.

I was wondering if someone could have a look at my attempt at calculating the resultant vector of 3 forces. Figure is here:http://tinypic.com/view.php?pic=2psrllz&s=6, and from the top down the forces are F1=24,9kN, F2=12,7kN and F3=21kN. The angles are(again from the top down) 56,4°, 15,3° and 40,6°.

I start by calculating the force in x-direction:

$Rx= 24,9*cos56,4°+12,7*cos15,3°+21*cos55,9° = 37,8kN$

y-direction:

$Ry= 24,9*sin56,4°-12,7*sin15,3°-21*sin55,9° = -7,15*10^-4$ -which is obviously wrong, but I can't see where the error is.

(English is not my first language, so I apologize for any word and grammar mistakes.)

rude man
Homework Helper
Gold Member
Why do you think it's "obviously wrong"?

I'm not 100% sure(I'm fairly new when it comes to mechanics and physics as a whole), but when I go on to calculate the resultant vector and the corresponding angle based on the numbers in my first post I get:

$R=\sqrt{Rx^2+Ry^2} = +\sqrt{37,8^2+(-7,158*10^-4)^2}≈37,8$

I then use inverse tan Ry/Rx to get the angle:

$tan^-1 Ry/rx = tan^-1 (-7,15*10^-4)/37,8 =-0,001°$

To me this looks like an unlikely answer, and when I try to enter them into the task I get a message with "wrong".(It's a web based service so I only get "right" or "wrong" - no indication of where I've made an error, so I'd really appreciate it if someone could take a look at my calculations.

rude man
Homework Helper
Gold Member
I'm not 100% sure(I'm fairly new when it comes to mechanics and physics as a whole), but when I go on to calculate the resultant vector and the corresponding angle based on the numbers in my first post I get:

QUOTE]

Your answers are essentially correct. I computed Ry = -7.16e-4, Rx = 37.80 and θ = -1.085e-3 deg = -0.001085 deg.