Question

Applying the Law of Conservation of Momentum

Answer 1

answer

the final velocity is half of train car B's initial velocity

explanation

the conservation of momentum states that the initial and final total momentum are equal

m1v1 + m2v2 for initial momentum

(m1 + m2)v3 for final momentum because both cars stick together so their masses are combined

m1v1 + m2v2 = (m1 + m2)v3

since the mass of both are the same, m1 = m2

m1v1 + m1v2 = (m1 + m1)v3

m1(v1 + v2) = 2m1v3

divide both sides by m1

v1 + v2 = 2v3

since train car A is initially at rest, v1 = 0

v2 = 2v3

v3 = v2 * 1/2

the final velocity is half of train car B's initial velocity