Carts A and B collide on a low-friction track. Rank, from largest to smallest, the following four collisions according to the magnitude of the change in the momentum of cart B, which has twice the inertia of cart A.

(a) A initially moving right at \(1.0 \mathrm{~m} / \mathrm{s}, B\) initially stationary; stick together on impact.

(b) A initially stationary, B initially moving left at \(1.0 \mathrm{~m} / \mathrm{s}\); stick together on impact.

(c) A initially moving right at \(1.0 \mathrm{~m} / \mathrm{s}\); after impact, A moving left at \(0.33 \mathrm{~m} / \mathrm{s}, B\) moving right at \(0.67 \mathrm{~m} / \mathrm{s}\).

(d) A initially moving right at \(1.0 \mathrm{~m} / \mathrm{s}, \mathrm{B}\) initially moving left at \(1.0 \mathrm{~m} / \mathrm{s}\); stick together on impact.