A 310-g air track cart is traveling at 1.25 m/s and a 260-g cart traveling in the opposite direction at 1.33 m/s.What is the speed of the center of mass of the two carts?
A) 2.80 m/s
B) 0.0732 m/s
C) 0.131 m/s
D) 1.47 m/s
E) 1.29 m/s

Question

Quizplus · Accepted Answer

The speed of the center of mass can be calculated using the formula: $v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$, where $m_1$ and $m_2$ are the masses of the carts, and $v_1$ and $v_2$ are their velocities. Given that one cart is moving in the opposite direction, its velocity is considered negative. Thus, $v_{cm} = \frac{(0.31 \times 1.25) + (0.26 \times -1.33)}{0.31 + 0.26} = \frac{0.3875 - 0.3458}{0.57} = 0.0731 \, m/s$, which rounds to 0.0732 m/s, making option B correct.

A 310-G Air Track Cart Is Traveling at 1