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.
ScanSolve AI Answer
Step 1: Name and state the principle illustrated. The principle illustrated is the Principle of Conservation of Linear Momentum. Statement: In an isolated system, the total linear momentum remains constant. Step 2: Calculate the combined mass of Ziphokazi and her car. This is an elastic collision, so both linear momentum and kinetic energy are conserved. Let Asisipho and her car be object 1, and Ziphokazi and her car be object 2. Let the direction to the left be negative. Given: Mass of Asisipho and her car, m_1 = 340 kg Initial velocity of Asisipho, v_1i = -2.4 m/s Initial velocity of Ziphokazi, v_2i = 0 m/s Final velocity of Asisipho, v_1f = -0.8 m/s Final velocity of Ziphokazi, v_2f = -V (where V is the magnitude of Ziphokazi's velocity) Mass of Ziphokazi and her car, m_2 = ? Using the principle of conservation of linear momentum: m_1 v_1i + m_2 v_2i = m_1 v_1f + m_2 v_2f (340 kg)(-2.4 m/s) + m_2(0 m/s) = (340 kg)(-0.8 m/s) + m_2(-V) -816 = -272 - m_2 V m_2 V = 816 - 272 m_2 V = 544 (Equation 1) For an elastic collision, the relative speed of approach equals the relative speed of separation: v_1i - v_2i = -(v_1f - v_2f) v_1i - v_2i = v_2f - v_1f (-2.4 m/s) - (0 m/s) = (-V) - (-0.8 m/s) -2.4 = -V + 0.8 -2.4 - 0.8 = -V -3.2 = -V V = 3.2 m/s Now substitute the value of V into Equation 1: m_2 (3.2 m/s) = 544 m_2 = (544)/(3.2) m_2 = 170 kg The combined mass of Ziphokazi and her car is 170 kg.