Classical Mechanics
# Momentum

Ball $A$ of mass $2\text{ kg}$ is rolling on a frictionless horizontal floor at $5\text{ m/s}.$ It collides head-on with ball $B$ of mass $3\text{ kg}$ which is initially at rest. If we let $v_A$ and $v_B$ denote the respective velocities of balls $A$ and $B$ after the collision, in which of the following situations are the linear momenta conserved?

Define the initial direction that ball $A$ moves in as positive direction.

$A$ of mass $m_A=2\text{ kg}$ moves with a velocity of $v=2\text{ m/s}$ toward a stationary object $B$ of mass $m_B=4\text{ kg}.$ After the impact, objects $A$ and $B$ move off in directions that form $30^\circ$ and $45^\circ$ angles with the initial direction of object $A,$ respectively. Assuming that the system is entirely frictionless, what is the speed of object $A$ after the collision?

Object