System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is -

Step-by-step solution

Method - I As cylinder will remain in contact with wedge A V x = 2 u As it also remain in contact with wedge B u sin 3 0 ∘ = V y cos 3 0 ∘ - V x sin 3 0 ∘ V y = V x sin 3 0 ∘ cos 3 0 ∘ + u sin 3 0 ∘ cos 3 0 ∘ V y = V x tan 3 0 ∘ + u tan 3 0 ∘ V y = 3 u tan 3 0 ∘ = 3 u V = V x 2 + V y 2 = 7 u Method - II In the frame of A 3 u sin 3 0 ∘ = V y cos 3 0 ∘ ⇒ V y = 3 u tan 3 0 ∘ = 3 u and V x = 2 u V = V x 2 + V y 2 = 7 u