Question

Two particles with masses 6m and 6m are moving toward each other along the x-axis with the same initial speeds vᵢ The particle with mass 6mis traveling to the left, and the particle with mass 6m is traveling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached. What are the final speeds of the particles?

A) vᵢ and vᵢ
B) vᵢ and -vᵢ
C) 0 and 0
D) 1/2vᵢ and 1/2vᵢ

Answer 1

In an elastic collision, both momentum and kinetic energy are conserved. The initial velocity of mass A is 5 m/s.

Step-by-step explanation:

In an elastic collision, both momentum and kinetic energy are conserved. Let's denote the initial velocity of mass A as v and the final velocity of mass B as vB. Since both objects have equal mass, the principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision:

mass A * initial velocity of A + mass B * initial velocity of B = mass A * final velocity of A + mass B * final velocity of B

mass A * v + mass B * (-v) = mass A * (-v) + mass B * vB (substituting the given values)

v = 5 m/s (solving for v)

Therefore, the initial velocity of mass A is 5 m/s.