Three particles A, B and C of respective masses m_(1), m_(2) and m_(3) lie on a smooth horizontal surface, and an fastened to two light inextensible strings as shown in Fig. The particle A is imparted an impulse J along vec(BA) . Find the initial speed of each particle.

Three particles A, B and C of respective masses m_(1), m_(2) and m_(3)

1.	Three particles A, B and C of respective masses m_(1), m_(2) and m_(3) lie on a smooth horizontal surface, and an fastened to two light inextensible strings as shown in Fig. The particle A is imparted an impulse J along vec(BA) . Find the initial speed of each particle.
Answer» SOLUTION :`J-J_(1)=m_(1)v_(1)` ………i `J_(1)-J_(2)(cos45^(@))=m_(2)v_(2y)`…………..ii `J_(2)sin45^(@)=m_(2)v_(2x)`…………..iii `J_(2)=m_(3)v_(3)` ……………iv. Now `v_(2y)=v_(1)` and `v_(2y)cos45^(@)-2_(2x)cos45^(@)=v_(3)` Solve to get `v_(y)=(sqrt2m_(2)J)/(m_(1)m_(3)+2m_(2)(m_(1)+m_(2)+m_(3)))` `v_(1)=((m_(3)+2m_(2))J)/(m_(1)m_(3)+2m_(2)(m_(1)m_(2)+m_(3)))` `v_(2x)=(m_(3)v_(3)cos45^(@))/m_(2)=(m_(3)J)/(m_(1)m_(3)+2m_(2)(m_(1)+m_(2)+m_(3)))` Net velocity of `m_(2)` `=sqrt(v_(1)^(2)+v_(2x)^(2))=(sqrt2(m_(2)^(2)+(m_(2)+m_(3))^(2))^(1//2))/(m_(1)m_(3)+2m_(2)(m_(1)+m_(2)+m_(3)))`