Question

One particle, of mass m , moves with a speed v in the x-direction, and another particle, of mass 2 m , moves with a speed v/2 in the y-direction. what is the velocity of the center of mass of these two particles?

Answer 1

Given :

One particle, of mass m , moves with a speed v in the x-direction, and another particle, of mass 2 m , moves with a speed v/2 in the y-direction.

To Find :

The velocity of the center of mass of these two particles.

Solution :

Speed of mass m, $v\ \hat i$.

Speed of mass 2m , $\dfrac{v}{2}\ \hat{j}$ .

Speed of center of mass is given by :

$v_{cm }= \dfrac{m\times( v\ \hat{i}) + 2m \times \dfrac{v}{2}\ \hat{j} }{m + 2m}\\\\v_{cm}=\dfrac{v( \hat{i} + \hat{j})}{3}$

Hence, this is the required solution.

Answer 2

The velocity of the center of mass of these two particles will be $\rm v_{cm}= \frac{v(\vec i+\vec j)}{3}$

What is velocity?

The change of displacement with regards to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

The given data in the problem is

$\rm V_i$ is the speed of mass m

$\rm \frac{v}{2} \hat j$ is the speed of mass 2m

Speed of the center of mass will be;

$\rm v_{cm}=\frac{m \times (v \hat i)+2m \times \frac{v}{2}\hat j }{m+2m} \\\\ \rm v_{cm}= \frac{v(\vec i+\vec j)}{3}$

Hence the  velocity of the center of mass of these two particles will be $\rm v_{cm}= \frac{v(\vec i+\vec j)}{3}$.

To learn more about the velocity refer to the link;

https://brainly.com/question/862972