Question

Two objects of mass 5kg and 3kg are moving in same direction with velocity 5m/s and 3m/s respectively. If they collide head on elastically find their velocities after collision.

Answer 1

consider 5 kg body as object 1 and 3 kg as object 2, their velocities v1 and v2 after collision and u1 and u2 before collision
initial momentum = p1
coefficient of restitution = e
e = (v2 - v1)/(u1 - u2)
thus;
e(u2 - u1)=(v2 - v1);v2=e(u2 - u1)+v1

p1=m1v1+m2v2
thus putting the previous equation;
p1=m1v1+m2(e(u2-u1)+v1)
p1=v1(m1+m2)+m2(e)(u1-u2)
thus ;
v1=(p1+(e)(m2)(u2-u1))/(m1+m2)
replacing the values we get
v1=((5*5+3*3)+(1)(3)(3-5))/(5+3)
v1=((34)+3(-2))/8
v1=(28)/8

and now we have
v2=e(u1-u2)+v1
v2=(5-3)+28/8
v2=2+28/8
v2=44/8

***here we have taken e=1 as we have that it elastical collision
we can confirm this by conservation of momentum
m1v1+m2v2=m1u1+m2u2
(5*28/8)+(3*44/8)=34
(140/8)+(132/8)=34
272/8=34
thus proved