Final answer:
The initial and final momentum of two masses in a collision can be found using conservation of momentum equations m1V1 + m2V2 = m1v'1 + m2v'2 for 1D, and m1V1 = m1v'1 cos θ1 + m2v'2 cos θ2 for 2D when one mass is at rest.
Step-by-step explanation:
The equations for the initial and final momentum of mass 1 (m1) and mass 2 (m2) can be derived from the law of conservation of momentum. For a one-dimensional collision, the equation is m1V1 + m2V2 = m1v'1 + m2v'2, where V represents initial velocities and v' represents final velocities. In a two-dimensional collision where one of the particles is initially at rest, the conservation of momentum along the x-axis is given by m1V1 = m1v'1 cos θ1 + m2v'2 cos θ2, and along the y-axis by 0 = m1v'1 sin θ1 + m2v'2 sin θ2.
To determine the change in momentum, these equations are used by substituting the known values for mass (m1 and m2) and for initial (V1, V2) and final velocities (v'1, v'2).