Answer:
v₁ = v₂ = v/2
Explanation:
- Assuming no external forces acting during the collision, total momentum must be conserved, as follows:
[tex]m_{1}* v = m_{1} *v_{1f} + m_{2}*v_{2f} (1)[/tex]
- If the collision is perfectly inelastic, both masses stick together after the collision, which means that both masses will have the same final speed:
[tex]v_{1f} = v_{2f} (2)[/tex]
- We know that both masses are equal each other:
[tex]m_{1} =m_{2} = m (3)[/tex]
- From (1), (2) and (3), we can solve for v₁f = v₂f, as follows:
[tex]m v = 2*m *v_{1f}[/tex]
⇒ [tex]v_{1f} = v_{2f} =\frac{v}{2}[/tex]
- The velocities of both objects after the collision are the same, and equal to v/2.
