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
4.1: Calculate the velocity of the car relative to the truck. Let the eastern direction be positive. Velocity of car, v_c = +20 m·s^-1 Velocity of truck, v_t = -20 m·s^-1 The velocity of the car relative to the truck is given by: v_c rel t = v_c - v_t v_c rel t = (+20 m·s^-1) - (-20 m·s^-1) v_c rel t = 20 m·s^-1 + 20 m·s^-1 v_c rel t = 40 m·s^-1 The velocity of the car relative to the truck is 40 m·s^-1 EAST. 4.2: State the principle of conservation of linear momentum in words. In an isolated system, the total linear momentum remains constant. 4.3: Calculate the velocity of the truck-car system immediately after the collision. Let the eastern direction be positive. Mass of car, m_c = m Initial velocity of car, v_ci = +20 m·s^-1 Mass of truck, m_t = 2m Initial velocity of truck, v_ti = -20 m·s^-1 Since the vehicles stick together, their final velocity will be the same, v_f. According to the principle of conservation of linear momentum: m_c v_ci + m_t v_ti = (m_c + m_t) v_f Substitute the given values: (m)(+20 m·s^-1) + (2m)(-20 m·s^-1) = (m + 2m) v_f 20m - 40m = 3m v_f -20m = 3m v_f Divide both sides by m: -20 = 3 v_f v_f = (-20)/(3) m·s^-1 v_f ≈ -6.67 m·s^-1 The negative sign indicates the direction is WEST. The velocity of the truck-car system immediately after the collision is 6.67 m·s^-1 WEST. 4.4.1: Determine, in terms of F, the magnitude of the force that the truck exerts on the car on impact. Give a reason for the answer. The magnitude of the force that the truck exerts on the car is F. Reason: According to Newton's Third Law, for every action, there is an equal and opposite reaction. The force exerted by the car on the truck is an action force, and the force exerted by the truck on the car is the reaction force. These forces are equal in magnitude and opposite in direction.