Three trolley carts are free to move on a one dimensional frictionless horizontal track. Cart A has a mass of 1.9 \mathrm{~kg} and an initial speed of 1.7 \mathrm{~m} / \mathrm{s} to the right; Cart B has a mass of 1.1 \mathrm{~kg} and an initial speed of 2.5 \mathrm{~m} / \mathrm{s} to the left; cart \mathrm{C} has a mass of 1.3 \mathrm{~kg} and is originally at rest. Collisions between carts \mathrm{A} and \mathrm{B} are perfectly elastic; collisions between carts \mathrm{B} and \mathrm{C} are perfectly inelastic.
\includegraphics[max width=\textwidth]{2024_06_26_609482864542c96cc3bag-04}What is the velocity of the center of mass of the system of the three carts after the last collision?
Answer Choices
A. 0.11 \mathrm{~m} / \mathrm{s}
B. 0.16 \mathrm{~m} / \mathrm{s}
C. 1.4 \mathrm{~m} / \mathrm{s}
D. 2.0 \mathrm{~m} / \mathrm{s}
E. 3.23 \mathrm{~m} / \mathrm{s}
