Question

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

Answer 1

Answer:

the speed of the center of mass of the two-particle system is 3.4 m/s.

Explanation:

Given that,

Mass of particle 1, m = 2 kg

Velocity of the particle 1, v = 4 m/s in +x direction

Mass of particle 2, m' = 3 kg

Velocity of the particle 2, v' = 5 m/s in +y direction.

The x -coordinate of velocity of the centre of mass is given by :

$v_x=\dfrac{mv+m'v'}{m+m'}\\\\v_x=\dfrac{2\times 4+3\times 0}{2+3}\\\\v_x=1.6\ m/s$

The y -coordinate of velocity of the centre of mass is given by :

$v_y=\dfrac{mv+m'v'}{m+m'}\\\\v_y=\dfrac{2\times 0+3\times 5}{2+3}\\\\v_y=3\ m/s$

So, the the speed of the center of mass of the two-particle system given by :

$v=\sqrt{v_x^2+v_y^2} \\\\v=\sqrt{1.6^2+3^2} \\\\v=3.4\ m/s$

So, the speed of the center of mass of the two-particle system is 3.4 m/s.