A \(0.30-\mathrm{kg}\) cart traveling along a low-friction track at \(2.0 \mathrm{~m} / \mathrm{s}\) relative to Earth collides with a \(0.50-\mathrm{kg}\) cart traveling in the same direction at \(1.0 \mathrm{~m} / \mathrm{s}\) relative to Earth. If the system's kinetic energy measured in the Earth reference frame increases by \(30 \%\) as a result of the explosive collision, what are the final velocities of the carts in this reference frame?