A car of mass 1600 kg traveling at 30 m/s collides with a minibus of mass 3000 kg traveling at 20 m/s in the opposite direction. They move together after the collision. Calculate their final velocity

$$m_C u_C + m_M u_M = (m_C + m_M) v_f$$ $$(1600 \text{ kg})(-30 \text{ m/s}) + (3000 \text{ kg})(20 \text{ m/s}) = (1600 \text{ kg} + 3000 \text{ kg}) v_f$$ $$-48000 \text{ kg}\cdot\text{m/s} + 60000 \text{ kg}\cdot\text{m/s} = (4600 \text{ kg}) v_f$$ $$12000 \text{ kg}\cdot\text{m/s} = (4600 \text{ kg}) v_f$$ $$v_f = \frac{12000 \text{ kg}\cdot\text{m/s}}{4600 \text{ kg}}$$ $$v_f \approx 2.60869 \text{ m/s}$$

The velocity of the two vehicles after the collision is $\boxed{\text{}2.61 \text{ m/s} \text{ to the right}\text{}}$

$$KE_f = \frac{1}{2} (m_C + m_M) v_f^2$$

Using the more precise value for $v_f = \frac{12000}{4600} \text{ m/s}$:

$$KE_f = \frac{1}{2} (1600 \text{ kg} + 3000 \text{ kg})\left(\frac{12000}{4600} \text{ m/s}\right)^2$$ $$KE_f = \frac{1}{2} (4600 \text{ kg})\left(\frac{120}{46} \text{ m/s}\right)^2$$ $$KE_f = 2300 \left(\frac{14400}{2116}\right)$$ $$KE_f = \frac{33120000}{2116}$$ $$KE_f \approx 15652.17 \text{ J}$$

Since $KE_i = 1320000 \text{ J}$ and $KE_f \approx 15652.17 \text{ J}$,

$$KE_i \neq KE_f$$

Therefore, kinetic energy is not conserved, and the collision was $\boxed{\text{}inelastic\text{}}$