According to first situation
Total momentum before collision,
pi‌=mvA+2mvB‌=m×150+2m×v=150m+2mv Since, coefficient of restitution,
e=1Hence, after collision, body
A transfer its complete velocity to body
B. hence, after collision velocity of body
B,v′=150−v.
Total momentum after collision,
pf‌=2mv′+m×0‌=2mv′‌=2m(150−v)According to law of conservation of momentum,
pi‌=pf150m+2mv‌=2m(150−v)150+2v‌=300−2v⇒4v=150⇒‌‌v‌=37.5m∕ s