Two balls with masses m_(1)=3 and m_(2)=5kg have initial velocities v_(1)=v_(2)=5m//s in the directions shown in figure. They collide at the origin. a. find the velocioty of the CM 3s before the collision. b. Find the position of the CM 2s after the collision.

Two balls with masses m_(1)=3 and m_(2)=5kg have initial velocities v_

1.	Two balls with masses m_(1)=3 and m_(2)=5kg have initial velocities v_(1)=v_(2)=5m//s in the directions shown in figure. They collide at the origin. a. find the velocioty of the CM 3s before the collision. b. Find the position of the CM 2s after the collision.
Answer» Solution :a. GIVEN time is of no consequence SINCE `v_(CM)` is fixed for all times `v_(CM)(x)=(m_(1)v_(1x)+m_(2)v_(2x))/(m_(1)+m_(2))` `=((3)(-5cos37^(@))+(5)(0))/(8kg)=-1.5m//s` `v_(CM)(y)=(m_(1)v_(1)y+m_(2)y_(2))/(m_(1)+m_(2))` `=(3)(-5sin37^(@))+(5xx5)/(8kg)=+2m//s` `:. vecv_(CM)=1.5hati+2hatjm//s` b. Since the collision occurs at the origin `(vecr_(1)=0)`, the position of the centre of mass `2s` later is `vecr_(CM)=vecr_(1)+vecv_(CM^(t))` `=vecv_(CM^(t))=-3hati+4hatjm`