Given that VB =2u, show that e=3/5

Question

Given that VB =2u, show that e=3/5

Asked on April 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-23T03:12:00.139Z

Step 1: Set up the equations for conservation of momentum and the coefficient of restitution. Let the initial direction of particle A be positive. Mass of particle A: $m_A = m$ Mass of particle B: $m_B = 3m$ Initial velocity of particle A: $u_A = 4u$ Initial velocity of particle B: $u_B = -u$ (since they are moving towards each other) Final velocities: $v_A$ and $v_B$ Conservation of momentum: $$m_A u_A + m_B u_B = m_A v_A + m_B v_B$$ $$m(4u)

Accepted Answer · 2026-04-23T03:12:00.139Z

Step 1: Set up the equations for conservation of momentum and the coefficient of restitution. Let the initial direction of particle A be positive. Mass of particle A: $m_A = m$ Mass of particle B: $m_B = 3m$ Initial velocity of particle A: $u_A = 4u$ Initial velocity of particle B: $u_B = -u$ (since they are moving towards each other) Final velocities: $v_A$ and $v_B$ Conservation of momentum: $$m_A u_A + m_B u_B = m_A v_A + m_B v_B$$ $$m(4u)

Given that VB =2u, show that e=3/5