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 :
[tex]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[/tex]
The y -coordinate of velocity of the centre of mass is given by :
[tex]v_y=\dfrac{mv+m'v'}{m+m'}\\\\v_y=\dfrac{2\times 0+3\times 5}{2+3}\\\\v_y=3\ m/s[/tex]
So, the the speed of the center of mass of the two-particle system given by :
[tex]v=\sqrt{v_x^2+v_y^2} \\\\v=\sqrt{1.6^2+3^2} \\\\v=3.4\ m/s[/tex]
So, the speed of the center of mass of the two-particle system is 3.4 m/s.
