1. **State the problem:** A body of mass 2 kg moving at 1 m/s meets another body of mass 3 kg moving at 2 m/s in the opposite direction. They stick together after collision. Find the velocity of the combined body. 2. **Formula used:** Use the law of conservation of momentum: $$m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f$$ where $m_1, m_2$ are masses, $v_1, v_2$ are initial velocities, and $v_f$ is the final velocity. 3. **Assign values and directions:** Let the direction of the first body be positive. $$m_1 = 2, v_1 = 1$$ $$m_2 = 3, v_2 = -2$$ (opposite direction) 4. **Apply the formula:** $$2 \times 1 + 3 \times (-2) = (2 + 3) v_f$$ $$2 - 6 = 5 v_f$$ 5. **Simplify:** $$-4 = 5 v_f$$ 6. **Solve for $v_f$:** $$v_f = \frac{-4}{5}$$ 7. **Interpret the result:** $$v_f = -0.8$$ m/s means the composite body moves at 0.8 m/s in the direction of the second body. **Final answer:** $$v_f = -0.8 \text{ m/s}$$ (0.8 m/s opposite to the first body's direction)