Given, m1=1kg u1=12ms−1 m2=2kg u2=−24ms−1 (-ve sign implies that, it is travelling in the opposite direction) e=
2
3
As we know, coefficient of restitution, e=
v2−v1
u1−u2
.
2
3
=
v2−v1
12+24
2
3
=
v2−v1
36
or v2−v1=24 ...(i) According to the law of conservation of momentum, Initial momentum of the system = Final momentum of the system ⇒ m1u1+m2u2=m1v1+m2v2 Substituting the given values in the above relation, we get 1×12+2×(−24)=1×v1+2v2 ⇒ 12−48=v1+2v2 ⇒ v1+2v2=−36 ...(ii) Solving Eqs.(i) and (ii), we get v2=−4ms−1 ⇒ −4−v1=24[∵ from Eq. (i) ] ⇒ v1=−24−4 =−28ms−1