Puck $A$ (mass $m_{A} )$ is moving on a frictionless, horizontal air table in the $+x$ -direction

with velocity $\vec{v}_{A 1}$ and makes an elastic, headon collision with puck $B\left(\text { mass } m_{B}\right),$ which is initially at rest. After the collision, both pucks are moving along the $x$ -axis. (a) Calculate the velocity of the center of mass of the two-puck system before the collision. (b) Consider a coordinate system whose origin is at the center of mass and moves with it. Is this an inertial reference frame? (c) What are the initial velocities $\vec{u}_{\Delta 1}$ and $\vec{u}_{B 1}$ of the two pucks in this center-of-mass reference frame? What is the total momentum in this frame? (d) Use conservation of momentum and energy, applied in the center-of-mass reference frame, to relate the final momentum of each puck to its initial momentum and thus the final velocity of each puck to its initial velocity. Your results should show that a one-dimensional, elastic collision has a very simple description in center-of-mass coordinates. (e) Let $m_{A}=0.400 \mathrm{kg}$ ,

$m_{B}=0.200 \mathrm{kg},$ and $v_{A 1}=6.00 \mathrm{m} / \mathrm{s}$ . Find the center-of-mass velocities $\vec{u}_{A 1}$ and $\vec{u}_{B 1},$ apply the simple result found in part (d),

and transform back to velocities in a stationary frame to find the final velocities of the pucks. Does your result agree with Eqs. $(8.24)$ and $(8.25) ?$