1. **State the problem:** A green marble moving at 0.7 m/s hits a stationary blue marble. After collision, the blue marble moves at 1.0 m/s. Both marbles have the same mass of 3.0 g. We need to find the final speed of the green marble. 2. **Relevant formula:** Since the collision involves two objects and no external forces, we use conservation of momentum: $$m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$$ where $m_1, m_2$ are masses, $v_{1i}, v_{2i}$ initial velocities, and $v_{1f}, v_{2f}$ final velocities. 3. **Given values:** - $m_1 = m_2 = 3.0$ g (equal masses) - $v_{1i} = 0.7$ m/s (green marble initial speed) - $v_{2i} = 0$ m/s (blue marble initially stationary) - $v_{2f} = 1.0$ m/s (blue marble final speed) - $v_{1f} = ?$ (green marble final speed, unknown) 4. **Apply conservation of momentum:** $$3.0 \times 0.7 + 3.0 \times 0 = 3.0 \times v_{1f} + 3.0 \times 1.0$$ 5. **Simplify:** $$2.1 = 3.0 v_{1f} + 3.0$$ 6. **Solve for $v_{1f}$:** $$3.0 v_{1f} = 2.1 - 3.0 = -0.9$$ $$v_{1f} = \frac{-0.9}{3.0} = -0.3$$ 7. **Interpretation:** The negative sign means the green marble moves in the opposite direction after collision with speed 0.3 m/s. **Final answer:** The green marble's final speed is $0.3$ m/s in the opposite direction.