Simple problem about relative motion.

[ParrotPete]

Homework Statement

A body consisting of two spheres attached by a 10 meter solid long rod is rolling down a 45 degree incline at one end while rolling up a 45 degree incline on the other end.
At the instant when the connecting rod is horizontal the sphere rolling down has the velocity 2 m/s down the incline and the acceleration 3 m/s^2 down the incline. At this time, what is the velocity of the sphere rolling up and what is the angular velocity of the rod?

Homework Equations

V_B = V_A+ωXr_B/A

The Attempt at a Solution

V_A=2*(cos(45)*e_i-sin(45)*e_j
V_B = V_B*(cos(45)*e_i+sin(45)*e_j)
r_A/B= 10*e_i
ω=ω*e_z
Doing the calculations
V_B cos(45) = cos(45)
V_B*sin(45) = -2*sin(45)+10ω

What am I doing wrong?

 

[haruspex]

V_A=2*(cos(45)*e_i-sin(45)*e_j
V_B = V_B*(cos(45)*e_i+sin(45)*e_j)

I guess that's V_B = v_B*(cos(45)*e_i+sin(45)*e_j), to avoid the pun.

r_A/B= 10*e_i

e_k, perhaps?

ω=ω*e_z

What's e_z? Do you mean e_i?

Doing the calculations
V_B cos(45) = cos(45)

You've lost me - where did that come from?