Question

question 21 of 25
two cars collide at an intersection. one car has a mass of 1600 kg and is moving 8 m/s to the north, while the other has a mass of 1400 kg and is moving 12 m/s to the south. what is their combined momentum?
a. 4000 kg·m/s north
b. 29,600 kg·m/s south
c. 29,600 kg·m/s north
d. 4000 kg·m/s south

Explanation:

Step1: Define north - positive direction

Let north be the positive direction. Then the velocity of the first car $v_1 = 8\ m/s$ and its mass $m_1=1600\ kg$, and the velocity of the second car $v_2=- 12\ m/s$ (negative as it moves south) and its mass $m_2 = 1400\ kg$.

Step2: Calculate momentum of each car

The momentum of the first car $p_1=m_1v_1=1600\times8 = 12800\ kg\cdot m/s$. The momentum of the second car $p_2=m_2v_2=1400\times(-12)=-16800\ kg\cdot m/s$.

Step3: Calculate combined momentum

The combined momentum $p = p_1 + p_2=12800+( - 16800)=-4000\ kg\cdot m/s$. The negative sign indicates the direction is south.

Answer:

D. 4000 kg·m/s south