Two bodies of mass 4 ~kg and 5 ~kg are moving along east and north directions with velocities 5 ~m / s and 3 ~m / s respectively. Magnitude of the velocity of centre of mass of the system is

Step-by-step solution

Velocity of centre of mass is v _ CM = m₁ v ₁+m₂ v ₂ m₁+m₂ Given, m₁=4 ~kg , m₂=5 ~kg , v₁=5 j m / s aligned & v₂=3 i m / s & v _ CM = 4 5 j +5 3 i 5+4 &= 20 i 9 + 15 9 j aligned Hence, magnitude | v _ CM |= ( 20 9 )^2+ ( 15 9 )^2 = 25 9 ~m / s