Vector A has a magnitude of 3.0 m and direction 1o3 degrees relative to the positive x-axis. Vector B has magnitude 5.0m and direction 215 relative to the positive x-axis.

Question

1) The resultant R=A + B has magnitude?

I did Rx= 3 cos 103 + 5 cos 215

Ry=3 sin 103 + 5 sin 215

Then sqrt Rx^2 + Ry^2 and got 4.77m.


Is this correct?

2) The resultant R has direction?

I do not know how to figure this out. Thank you

Answer 1

Hmmmm. Relative to positive x axis. So,

Rx=3cos103+5cos215 yes
Rx=-.6749-4.09=about -4.76 which is indicating your answer is wrong. R has to be bigger than A. Look at Ry

Ry=3*sin103 + 5*sin215=2.93-2.86=.06

so your answer is probably correct.

Answer 2

so for the direction of the resultant R would it be between 90 and 180 degrees?

Answer 3

Actually I think that the direction would be between 180 and 270 degrees since the R is bigger than A but less than B. Would you agree?