A \(1.00-\mathrm{kg}\) cart 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 a \(2.00-\mathrm{kg}\) cart traveling to the left at the same speed \(v\). The explosive goes off when the carts hit, causing them to rebound from each other. 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 each cart? Solve in the zeromomentum reference frame and then check your result by solving in the Earth reference frame.