Homework Statement
The resultant of vectors A and B has a magnitude of 20 units. A has a magnitude of 8 units, and the angle between A and B is 40 degrees. Calculate the magnitude of B.
Homework Equations
Trig, resolving vector components.
The Attempt at a Solution
I worked out the equations and got |B| = 13.20 units. But, this isn't any of my choices. Am I right, or am I missing something here?
Sure. Align A along the +x axis, with B at 40 degrees above that.
Then:
Ax = 8
Ay = 0
Bx = Bcos(40)
By = Bsin(40)
So Rx = 8+Bcos(40)
Ry = Bsin(40)
The magnitude of the resultant R would be sqrt(Rx^2 + Ry^2), which is equal to 20, so
20 = sqrt((8+Bcos(40))^2 + (Bsin(40))^2). Solving for B yields 13.20.
For the record, my choices were
12.6
16.2
14.8
18.4
But I don't see how you could get any of them.
Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.
Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.
