A system of inertia \(0.50 \mathrm{~kg}\) consists of a spring gun attached to a cart. The system is at rest on a horizontal low-friction track. A \(0.050-\mathrm{kg}\) projectile is loaded into the gun, then launched at an angle of \(40^{\circ}\) with respect to the horizontal plane. With what speed does the cart recoil if the projectile rises \(2.0 \mathrm{~m}\) at its maximum height?