Block C is suspended from a massless rigid bar with a length

Block C is suspended from a massless rigid bar with a length L attached to cart A that can roll freely on a frictionless horizontal track. Clay B with an initial horizontal velocity v_1 hits and adheres to the block. If the cart and the block is at rest before the hit, determine the velocity of C as it reaches its maximum elevation. The mass of cart A is m_A; the mass of clay B is m_B; the mass of block C is m_C. Neglect the sizes of the cart, the clay and the block.

Solution

Use Conservation of momentum.

Initial momentum MB*V1

Final momentum (when Block C is at the top of the swing and has Velocity ZERO)

(MA+MB+MC) * V2 where V2 is the final common velocity in the linear direction

V2 = MC/(MA+MC+MC)

(note energy is not conserved )