Question

Ball A travelling with velocity v collides head on with a stationary ball B. What is the velocity of ball B immediately after impact if the two balls have equal masses?

Answer 1

From the law of conservation of momentum, we have:

$$m_Av_{A,i}=m_Av_{A,f}+m_Bv_{B,f}.$$

Let's suppose that the kinetic energy is conserved. Then, we can write:

$$\dfrac{1}{2}m_Av_{A,i}^2=\dfrac{1}{2}m_Av_{A,f}^2+\dfrac{1}{2}m_Bv_{B,f}^2.$$

This formula gives us an addititional relationship between velocities. Therefore, with the help of these two formulas we can find the velocity of ball B immediately after impact. Since $m_A=m_B=m$ and $v_{A,i}=v$, we get:

$$v_{B,f}=\dfrac{2m_Av_{A,i}}{(m_A+m_B)}=\dfrac{2mv}{2m}=v.$$