The discussion revolves around calculating the magnitude of vector B given the resultant of vectors A and B, with specific magnitudes and an angle between them. The problem involves vector resolution and trigonometric relationships.
Some participants express confidence in their calculations, noting that they arrived at the same magnitude for vector B. There is an acknowledgment of potential discrepancies with the answer choices provided, leading to speculation about possible errors in those choices.
Participants mention the angle between vectors A and B and the resultant vector's magnitude, indicating that these parameters are critical to their calculations. There is a shared concern regarding the validity of the answer choices given the calculated result.
Ampere said: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?
Ampere said: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.
Dick said: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.
Dick said: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.