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I think this is a long method...Q.8
Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(2m)(u) + (m)(-u) = (2m)(v₁) + (m)(v₂)
2mu - mu = 2mv₁ + mv₂
mu = 2mv₁ + mv₂
u = 2v₁ + v₂ . . . . . (i)
e = 1 , as collision is elastic
e = (v₂ - v₁)/(u₁ - u₂)
1 = (v₂ - v₁)/(u₁ - u₂)
v₂ - v₁ = u₁ - u₂
v₂ - v₁ = u - (-u)
v₂ - v₁ = 2u
v₂ = 2u + v₁
Substitute in (i)
u = 2v₁ + (2u + v₁)
u = 3v₁ + 2u
3v₁ = -u
[ v₁ = -u/3 ]
v₂ = 2u + v₁
v₂ = 2u - u/3
[ v₂ = 5u/3 ]
So answer: A