Question

object a is moving to the right with a velocity of + 5m/s and strikes object B which is initially at rest in an elastic collision. object a and b have equal mass. what is the final velocity of object b

Answer 1

From the law of conservation of momentum, we have:

$$m_au_a=m_av_a+m_bv_b. (1)$$

Since collision is elastic, kinetic energy is conserved and we can write:

$$\dfrac{1}{2}m_1u_1^2=\dfrac{1}{2}m_1v_1^2+\dfrac{1}{2}m_2v_2^2. (2)$$

This formula gives us an additional relationship between velocities. Therefore, with the help of these two formulas we can find the final velocity of object $b$ after collision:

$$v_b=\dfrac{2m_1u_a}{(m_1+m_2)}=\dfrac{2m_1u_a}{2m_1}=u_a=5\ \dfrac{m}{s}.$$