Question

Physics help. Vector A⃗ points in the negative x direction. Vector B⃗ points at an angle of 27.0∘ above the positive x axis. Vector C⃗ has a magnitude of 10m and points in a direction 40.0∘ below the positive x axis.
Given that A⃗ +B⃗ +C⃗ =0, find the magnitudes of A⃗ and B⃗ .
Express your answer using two significant figures.

Can you please show work?

Answer 1

\[R = \sum F = A + B + C = 0\]
\[\sum F _{x} = 0 = A _{x}+B _{x}+C_{x}\]
\[\sum F _{y}=0=A _{y}+B _{y}+C _{y}\]

Answer 2

\[A = <-\left| \left| A \right| \right|, 0>\]
\[B = <\left| \left| B \right| \right|\cos(27), \left| \left| B \right| \right|\sin(27)>\]
\[C = <10\cos(40), -10\sin(40)>\]

Answer 3

Set up two equations, sum of x direction forces, and sum of y direction forces, both equal zero since it is in equilibrium.
The two unknown values are the magnitudes of vectors A and B.

Answer 4

Thank you so much!