The angular acceleration of the ladder can be found using the equation:
α = (2μg sinθ)/(3l)
where μ is the coefficient of kinetic friction, g is the acceleration due to gravity, θ is the angle between the ladder and the wall, and l is the length of the ladder.
Plugging in the given values, we get:
α = (2*0.2*32.2 sin 40)/(3*30) = 0.51 rad/s²
The forces at points A and B can be found using the equations for force and torque equilibrium:
ΣF_x = 0: FA cos(θ) - FB cos(θ) - F_friction = 0
ΣF_y = 0: FA sin(θ) + FB sin(θ) - W = 0
Στ = 0: FA sin(θ) l/2 - FB sin(θ) l/2 - W l/3 = 0
where W is the weight of the ladder.
Solving these equations simultaneously, we get:
FA = 31.8 lb ∠ 78.7 degrees
FB = 13.8 lb ∠ 169 degrees
Note: The values of FA and FB are consistent with the fact that the ladder is sliding down the wall. The force at point A is larger than the force at point B, which is due to the frictional force opposing the motion of the ladder.