Question

A 50 kg object moving at 15 m/s collides with another 50 kg object moving in the same direction at 10 m/s. If the collision is inelastic, what is the final velocity of the two objects after they combine?

Answer 1

12.5 m/s

Step-by-step explanation:

By conservation of momentum, we have that:

`\displaystyle m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'`

Because the two objects combine after collision, they will have the same velocity:

`\displaystyle m_1v_1 + m_2v_2 = (m_1+m_2)v_f`

Substitute and solve for final velocity:

`\displaystyle \begin{aligned} (50 \text{ kg})(15\text{ m/s}) + (50\text{ kg})(10\text{ m/s}) & = ((50+50)\text{ kg})v_f \\ \\ v_f & = 12.5\text{ m/s}\end{aligned}`

In conclusion, the final velocity of the system will be 12.5 m/s.