Addition of vectors by means of components..just need someone to check if answer is right?

Two forces are applied to a tree stump to pull it out of the ground. Force Fa has a magnitude of 2240 newtons and points 34.0 degrees south of east while force Fb has a magnitude of 3160 newtons and points due south. Using the component method, find the magnitude and direction of the resultant force Fa+Fb that is applied to the stump. Specify the direction with respect to due east.








So first I used Pythg Th. to get the resultant force


C=3873.39 N





and then the arc tan 3160/2240=54.6 degrees S of E

Addition of vectors by means of components..just need someone to check if answer is right?
The two forces are not at right angles to each other, so you cannot treat them that way. You can set up a triangle with the two vectors as two sides and the result vector as the other side. Using basic geometry, you can find that the angle between the two vectors is 124º. You can then use the cosine law to find the length of the remaining side:





l²=2240²+3160²


-2(2240)(3160)cos(124º)


l=4787N





and you can use the sine law to get the angle:


sin(x)=3160sin(124º)/4787


x=33º


Remember that this is an angle relative to your starting angle, so the direction of the resultant force is 34º+33º=77º S of E.
Reply:That is not the component method.


Say you are on an x,y grid y axis positve being due north, 0°, and x axis + being due east.


The component method would break each vector down into components along on the x and the y axis (two components each), so that you could just add these to get the resultant.


For instance, if the x component of a vector were 1, and the y component were 1, then the vector would be √2 long, 45° in quadrant I.


You are using the head to tail method, I believe.

curse of the golden flower