Show that the ratio of velocities of equal masses in an inelastic collision when one of masses is stationary is v_(1)/v_(2)=(1-e)/(1+e)

Show that the ratio of velocities of equal masses in an inelastic coll

1.	Show that the ratio of velocities of equal masses in an inelastic collision when one of masses is stationary is v_(1)/v_(2)=(1-e)/(1+e)
Answer» Solution :`e=("velocity of speration" ("after collision"))/("velocity of APPROACH" ("before collision"))` `=((v_(2)-v_(1)))/((u_(1)-u_(2)))=((v_(2)-v_(1)))/((u_(1)-0))=(v_(2)-v_(1))/u_(1)` implies `v_(2)-v_(1)=eu_(1)` From the law of conservation of linear momentum, `mu_(1)=mv_(1)+mv_(2)impliesu_(1)=v_(2)` Using the equation (2) for `u_(1) `in (1), we GET `v_(2)-v_(1)=e(v_91)+v_(2)` On simplification, we get `v_(1)/v_(2)=(1-e)/(1+e)`