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» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`J-J_(1)=m_(1)v_(1)` ………i <br/> `J_(1)-J_(2)(cos45^(@))=m_(2)v_(2y)`…………..ii <br/> <img src="https://d10lpgp6xz60nq.cloudfront.<klux>NET</klux>/physics_images/BMS_VOL2_C01_E01_061_S01.png" width="80%"/> <br/> `J_(2)sin45^(@)=m_(2)v_(2x)`…………..iii <br/> `J_(2)=m_(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)v_(3)` ……………iv. <br/> Now `v_(2y)=v_(1)` and `v_(2y)cos45^(@)-2_(2x)cos45^(@)=v_(3)` <br/> Solve to get `v_(y)=(sqrt2m_(2)J)/(m_(1)m_(3)+2m_(2)(m_(1)+m_(2)+m_(3)))` <br/> `v_(1)=((m_(3)+2m_(2))J)/(m_(1)m_(3)+2m_(2)(m_(1)m_(2)+m_(3)))` <br/> `v_(2x)=(m_(3)v_(3)cos45^(@))/m_(2)=(m_(3)J)/(m_(1)m_(3)+2m_(2)(m_(1)+m_(2)+m_(3)))` <br/> Net velocity of `m_(2)` <br/> `=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)))`</body></html>