Question

9. A car driving on the highway has a mass M and a velocity v. A truck on the highway has a mass 2M. If the truck has the same velocity v as the car, how does the momentum of the truck compare to the momentum of the car? a. b. If the truck as the same momentum as the car, how does the velocity of the truck compare to the velocity of the car *Now, assume the truck is driving in the opposite direction as the car (i.e., the truck will now have negative velocity). If the truck is driving with a velocity-v, what is the Total Momentum of the truck-car system? C. d. *"If the truck is driving in the opposite direction as the car, what must be the velocity of the truck (in terms of v) such that the total momentum of the truck-car system is zero?

Answer 1

momentum = mass * velocity

(a) Momentum of car p_c = m v momentum of truck p_t = 2 m v = 2 p_c implies p_t = 2 p_c (b) If velocity of truck is v_t then momentum of truck p_t^1 = 2 m v_t But p_t^1 = p_c = m v implies 2 m v_t = m v implies v_t = v/2 implies v_t = v/2 (c) total momentum p_T = m v + 2 m (-v) = -m v implies p_T = -m v (d) 0 = m v + 2 m u implies v = -2 u implies u = -v/2 implies u = -v/2