Cart A of inertia m has attached to its front end a device that explodes when it hits anything, releasing a quantity of energy E. This cart is moving to the right with speed v when it collides head-on with cart B of inertia 2m traveling to the left at the same speed v. The explosive goes off when the carts hit, causing them to rebound from each other. The initial direction of motion of cart A (to the right) is the +x direction.
If one-quarter of the explosive energy is dissipated into the incoherent energy of noise and deformation of the carts, what is the final velocity of cart A? in E,v,m

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