This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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2008 Exemplar Paper 1 Q 2 2.1 Step 1: Identify the given values and define a positive direction. Let right be the positive direction. Mass of car m_C = 1600 kg Initial velocity of car u_C = -30 m/s (to the left) Mass of minibus m_M = 3000 kg Initial velocity of minibus u_M = 20 m/s (to the right) The vehicles move together after the collision, so they have a common final velocity v_f. Step 2: Apply the principle of conservation of linear momentum. m_C u_C + m_M u_M = (m_C + m_M) v_f (1600 kg)(-30 m/s) + (3000 kg)(20 m/s) = (1600 kg + 3000 kg) v_f -48000 kg·m/s + 60000 kg·m/s = (4600 kg) v_f 12000 kg·m/s = (4600 kg) v_f v_f = 12000 kg·m/s4600 kg v_f ≈ 2.60869 m/s The velocity of the two vehicles after the collision is 2.61 m/s to the right 2.2 Step 1: Calculate the total initial kinetic energy. KE_i = (1)/(2) m_C u_C^2 + (1)/(2) m_M u_M^2 KE_i = (1)/(2) (1600 kg)(-30 m/s)^2 + (1)/(2) (3000 kg)(20 m/s)^2 KE_i = (1)/(2) (1600)(900) + (1)/(2) (3000)(400) KE_i = 800(900) + 1500(400) KE_i = 720000 J + 600000 J KE_i = 1320000 J Step 2: Calculate the total final kinetic energy. KE_f = (1)/(2) (m_C + m_M) v_f^2 Using the more precise value for v_f = (12000)/(4600) m/s: KE_f = (1)/(2) (1600 kg + 3000 kg)((12000)/(4600) m/s)^2 KE_f = (1)/(2) (4600 kg)((120)/(46) m/s)^2 KE_f = 2300 ((14400)/(2116)) KE_f = (33120000)/(2116) KE_f ≈ 15652.17 J Step 3: Compare initial and final kinetic energies. Since KE_i = 1320000 J and KE_f ≈ 15652.17 J, KE_i ≠ KE_f Therefore, kinetic energy is not conserved, and the collision was inelastic