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.
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
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.
so for the direction of the resultant R would it be between 90 and 180 degrees?
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?
Yes, your calculation for the magnitude of the resultant vector R is correct. To find the angle or direction of the resultant vector, you can use trigonometry. It is important to note that the angle is measured relative to the positive x-axis.
To find the direction of the resultant vector R, you can use the inverse tangent function (tan^(-1)) of the y-component (Ry) divided by the x-component (Rx) of the resultant vector.
In your case, Rx = 3 cos 103 + 5 cos 215 = -1.93
And Ry = 3 sin 103 + 5 sin 215 = -1.29
Using these values, you can calculate the angle or direction of the resultant vector R:
Angle = tan^(-1)(Ry/Rx)
= tan^(-1)(-1.29/-1.93)
≈ 33.8 degrees
Therefore, the direction of the resultant vector R is approximately 33.8 degrees relative to the positive x-axis.