Question

a) Derive the expression for velocities of the bodies after the elastic collision in one dimension.​

Answer 1

Answer: here is your answer

Explanation:

In Case of the Elastic Collision, Kinetic Energy before and after the collision remains the conserved, momentum also remains conserved.  

On This basis, Derivation in One dimension is shown in attachment.

The body of mass m₁ is moving with the velocity u₁ and body of mass m₂ is moving with velocity u₂, after the collision there velocity became v₁ and v₂.

The Final Result is,

v₂ - v₁ = u₁ - u₂.

Answer 2

Answer:

v2-v1=u1-u2

Explanation:

in elastic collision the momentum is conserved so we have

M1U1+M2U2=M1V1+M2V2 -------> 1

Kinetic energy is also conserved

m1u1^2+1/2m2u2^2=m1v1^2+m2v2^2--------2

from equ one we have

M1(U1-V1)=M2(U2-V2)--------->3

Now from equ two we have

M1(U1^2-V1^2)=M2(U2^2-V2^2)---------4

dividing equ 4 by 3

U1^2-V1^2. V2^2-U2^2

________ = _________

U1-V1. V2-U2

U1+V1=V2+U2

U1-U2=V2-V1

Hence verified