Question

A 3.5 metric ton truck moving at 9 m/s collides head on with a 900 kg car travelling at 16 m/s in the opposite direction. If the two vehicles stick together after the collision, what will be their common velocity just after the collision?

Answer 1

Let's apply the law of conservation of energy:

$$m_1v_1-m_2v_2=(m_1+m_2)v_c,$$ $$v_c=\dfrac{m_1v_1-m_2v_2}{m_1+m_2},$$ $$v_c=\dfrac{3500\ kg\cdot9\ \dfrac{m}{s}-900\ kg\cdot16\ \dfrac{m}{s}}{3500\ kg+900\ kg}=3.88\ \dfrac{m}{s}.$$

The sign plus means that the two vehicles moves in the positive direction (to the right).