Two carts A and B collide on a low-friction track. Measurements show that their initial and final momenta are \(\vec{p}_{\mathrm{A}, \mathrm{i}}=(+3.0 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}) \hat{\imath}, \vec{p}_{\mathrm{A}, \mathrm{f}}=(+1.0 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}) \hat{\imath}, \vec{p}_{\mathrm{B}, \mathrm{i}}=\) \((+2.0 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}) \hat{i}\), and \(\hat{p}_{\mathrm{B}, \mathrm{f}}=(-6.0 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}) \hat{i}\).

(a) What is the change in the momentum of each cart during the collision?

(b) What is the sum of these changes in momenta?

(c) Is this collision consistent with the physics you know? Why or why not?