Two perfectly elastic sphere of masses 2 kg and 3 kg moving in opposite directions with velocities after 8ms−1 and 6ms−1 respectively collide with each other. Find their velocities after the impact

Here m1=2kg,m2=3kg,u1=8ms−1,u2=−6 ms−1 According to the law of conservation of linear momentum; m1u1+m2u2=m1v1+m2v2 i.e., (2)(8)+(3)(−6)=2v1+3v2⇒2v1+3v2=−2 ...(i) Since the collision is elastic, u1−u2=v2−v1 i.e., 8−(−6)=v2−v1⇒v2−v1=14 .......(iii) On solving the equations (i) and (ii) we get v1=−8.8 ms−1,v2=5.2ms−1