Rank the following objects from highest to lowest in terms of momentum and from highest to lowest in terms of energy. a) an asteroid with mass \(10^{6} \mathrm{~kg}\) and speed \(500 \mathrm{~m} / \mathrm{s}\) b) a high-speed train with a mass of \(180,000 \mathrm{~kg}\) and a speed of \(300 \mathrm{~km} / \mathrm{h}\) c) a 120 -kg linebacker with a speed of \(10 \mathrm{~m} / \mathrm{s}\) d) a 10 -kg cannonball with a speed of \(120 \mathrm{~m} / \mathrm{s}\) e) a proton with a mass of \(6 \cdot 10^{-27} \mathrm{~kg}\) and a speed of \(2 \cdot 10^{8} \mathrm{~m} / \mathrm{s}\).

a) Asteroid: - Mass: \(m_a = 10^6 \,\mathrm{kg}\) - Velocity: \(v_a = 500 \,\mathrm{m/s}\) b) Train: - Mass: \(m_b = 180,000 \,\mathrm{kg}\) - Velocity: \(v_b = 300 \,\mathrm{km/h}\) Convert to m/s: \(v_b = \frac{300\,\mathrm{km}}{3.6\,\mathrm{h}} = 83.33\,\mathrm{m/s}\) c) Linebacker: - Mass: \(m_c = 120 \,\mathrm{kg}\) - Velocity: \(v_c = 10\,\mathrm{m/s}\) d) Cannonball: - Mass: \(m_d = 10 \,\mathrm{kg}\) - Velocity: \(v_d = 120 \,\mathrm{m/s}\) e) Proton: - Mass: \(m_e = 6 \cdot 10^{-27} \,\mathrm{kg}\) - Velocity: \(v_e = 2 \cdot 10^8 \,\mathrm{m/s}\) Now, calculate the momentum and energy for each object: Object a: \(p_a = m_a \cdot v_a = 10^6 \,\mathrm{kg} \cdot 500 \,\mathrm{m/s} = 5 \cdot 10^8\,\mathrm{kg\cdot m/s}\) \(E_a = \frac{1}{2} \cdot m_a \cdot v_a^2 = \frac{1}{2} \cdot 10^6 \,\mathrm{kg} \cdot (500 \,\mathrm{m/s})^2 = 1.25 \cdot 10^{11}\,\mathrm{J}\) Object b: \(p_b = m_b \cdot v_b = 180,000 \,\mathrm{kg} \cdot 83.33 \,\mathrm{m/s} = 1.5 \cdot 10^7\,\mathrm{kg\cdot m/s}\) \(E_b = \frac{1}{2} \cdot m_b \cdot v_b^2 = \frac{1}{2} \cdot 180,000 \,\mathrm{kg} \cdot (83.33 \,\mathrm{m/s})^2 = 6.25 \cdot 10^8\,\mathrm{J}\) Object c: \(p_c = m_c \cdot v_c = 120 \,\mathrm{kg} \cdot 10 \,\mathrm{m/s} = 1200\,\mathrm{kg\cdot m/s}\) \(E_c = \frac{1}{2} \cdot m_c \cdot v_c^2 = \frac{1}{2} \cdot 120 \,\mathrm{kg} \cdot (10 \,\mathrm{m/s})^2 = 6,000\,\mathrm{J}\) Object d: \(p_d = m_d \cdot v_d = 10 \,\mathrm{kg} \cdot 120 \,\mathrm{m/s} = 1200\,\mathrm{kg\cdot m/s}\) \(E_d = \frac{1}{2} \cdot m_d \cdot v_d^2 = \frac{1}{2} \cdot 10 \,\mathrm{kg} \cdot (120 \,\mathrm{m/s})^2 = 72,000\,\mathrm{J}\) Object e: \(p_e = m_e \cdot v_e = 6 \cdot 10^{-27} \,\mathrm{kg} \cdot 2 \cdot 10^8 \,\mathrm{m/s} = 1.2 \cdot 10^{-18}\,\mathrm{kg\cdot m/s}\) \(E_e = \frac{1}{2} \cdot m_e \cdot v_e^2 = \frac{1}{2} \cdot 6 \cdot 10^{-27} \,\mathrm{kg} \cdot (2 \cdot 10^8 \,\mathrm{m/s})^2 = 1.2 \cdot 10^{-10}\,\mathrm{J}\)

Now that we have calculated the momentum and energy values for each object, let's rank the objects from highest to lowest based on these values. Momentum Ranking (highest to lowest): 1. Object a (Asteroid): \(5 \cdot 10^8\,\mathrm{kg\cdot m/s}\) 2. Object b (Train): \(1.5 \cdot 10^7\,\mathrm{kg\cdot m/s}\) 3. Object c (Linebacker): \(1200\,\mathrm{kg\cdot m/s}\) 4. Object d (Cannonball): \(1200\,\mathrm{kg\cdot m/s}\) 5. Object e (Proton): \(1.2 \cdot 10^{-18}\,\mathrm{kg\cdot m/s}\) Energy Ranking (highest to lowest): 1. Object a (Asteroid): \(1.25 \cdot 10^{11}\,\mathrm{J}\) 2. Object b (Train): \(6.25 \cdot 10^8\,\mathrm{J}\) 3. Object d (Cannonball): \(72,000\,\mathrm{J}\) 4. Object c (Linebacker): \(6,000\,\mathrm{J}\) 5. Object e (Proton): \(1.2 \cdot 10^{-10}\,\mathrm{J}\)