At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system?
A) 3.8 m/s
B) 3.4 m/s
C) 5.0 m/s
D) 4.4 m/s
E) 4.6 m/s

Question

Quizplus · Accepted Answer

The velocity of the center of mass of a two-particle system can be found using the formula:

$v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$

Plugging in the given values, we get:

$v_{cm}=\frac{(2.0 kg)(4.0 m/s) + (3.0 kg)(5.0 m/s)}{2.0 kg + 3.0 kg}$

$v_{cm}=\frac{8.0 kg\cdot m/s + 15.0 kg\cdot m/s}{5.0 kg}$

$v_{cm}=4.6 m/s$

Therefore, the answer is B, 3.4 m/s.

At the Instant a 2