Question

Two particles of mass m and 2m moving in opposite direction collide elastically with v and 2v respectively. If the velocity of particle 1 and particle 2 is v1 and v2 respectively after collision then

Answer 1

Hey mate,
I assume you want to know v1 & v2.

◆ Answer-
v1 = 17/5 v
v2 = 4/5 v

◆ Explanation-
# Given-
m1 = m
m2 = 2m
u1 = v
u2 = 2v

# Solution-
In elastic collision, total momentum is conserved.
m1u1 + m2u2 = m1v1 + m2v2
m.v + 2m.2v = mv1 + 2mv2
v1 + 2v2 = 5v ...(1)

Here, kinetic energy is also conserved.
1/2 m1u1^2 + 1/2 m2u2^2 = 1/2 m1v1^2 + 1/2 m2v2^2
m.v^2 + 2m.(2v)^2 = mv1^2 + 2mv2^2
9v^2 = v1^2 + 2v2^2 ...(2)
9v^2 = (v1+2v2)(v1-2v2)

Substitute values from eqn (1),
9v^2 = 5v(v1-2v2)
v1-2v2 = 9/5 v ...(3)

Solving (1) & (3),
v1 = 17/5 v
v2 = 4/5 v

Hope that is helpful...

Answer 2

Answer:

Explanation:

Good luck !!