Dynamics with Polar coordinates

[Larrytsai]

Hey guys,
I have attached the question with the diagram.
So far i have found my magnitude of velocity = 90mm/s.
im just really stuck now, i can't find my angle to find my components Vr and V(theta)
I also know that you can solve this problem by finding a relationship between theta and "r", with the cosine law, but i have done that method, and i want to figure this out the way that is applicable to all questions. Thnx =)

 

[tiny-tim]

Hey Larrytsai!

(have a theta: θ and a beta: β )

… i want to figure this out the way that is applicable to all questions. Thnx =)

General method: just be logical, draw any right-angles you need to help you, and give everything names.

So draw the perpendicular from A to BC, call the foot of that perpendicular D, and use elementary trig.

 

[rl.bhat]

According to cosine rule
r^2 = a^2 + b^2 -2*a*b*cosβ.
Find the derivative to get dr/dt. Find the second derivative to find d^2r/dt^2
Next according to sine rule
r/sinβ = a/sinθ or
r*sinθ = a*sinβ
Find the derivative to get dθ/dt. The second derivative will give you the remaining answers.