A cart of mass \(m\) travels with speed \(v_0\) along a horizontal, frictionless track toward a stationary cart of mass \(2m\). The collision is tested under two different experimental conditions: in Setup 1, the collision is perfectly elastic, and in Setup 2, the carts latch together in a completely inelastic collision. The initial kinetic energy of the system before each collision is \(K_0\). Which row in the table correctly compares the magnitude of the impulse \(J_{\text{target}}\) delivered to the cart of mass \(2m\), the total final kinetic energy \(K_f\) of the system in Setup 2, and the post-collision center-of-mass speed \(v_{\text{cm}}\) of the system?

Row	Impulse on Target Cart	Final Kinetic Energy in Setup 2	Post-Collision Center-of-Mass Speed
A	\(J_1 = J_2\)	\(K_f = \dfrac{1}{3} K_0\)	\(v_{\text{cm},1} = v_{\text{cm},2}\)
B	\(J_1 = 2J_2\)	\(K_f = \dfrac{2}{3} K_0\)	\(v_{\text{cm},1} = v_{\text{cm},2}\)
C	\(J_1 = 2J_2\)	\(K_f = \dfrac{1}{3} K_0\)	\(v_{\text{cm},1} = v_{\text{cm},2}\)
D	\(J_1 = \dfrac{1}{2}J_2\)	\(K_f = \dfrac{1}{3} K_0\)	\(v_{\text{cm},1} > v_{\text{cm},2}\)