Question

Show that in the case of one dimensional elastic collision, the relative velocity of

approach of two colliding bodies before collision is equal to the relative velocity of

Separation after collision.​

Answer 1

Answer:

Refer image.

Here, for collision to happen, V

1

>V

2

velocity of approach =U

1

−U

2

[velocity w.r.t]

velocity of separation =V

2

−V

2

[vel.w.r.t]

As we know,

Coefficient of restitution (e) =

vel.ofapproach

vel.ofseperation

∴e=

U

1

−U

2

V

2

−V

1

........(1)

and, e=1 for elastic collision.

1=

U

1

−U

2

V

2

−V

1

U

1

−U

2

=V

2

−V

1

.

So,

velocity of approach=velocity of separation