A small ball of mass 1 kg moving with a velocity of 12 m/s

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be ______.

For elastic collision m₁u₁ + m₁u₂ = m₁v₁ + m₂v₂ ...(i)
By Moment conservation principle,
m₁ = 1 kg u₁ = 12 m/s
m₂ = 2 kg u₂ = 0 m/s

1	m₁u²₁ +	1	m₂u²₂ =	1	m₁v²₁ +	1	m₂v²₂.........(II)
2		2		2		2

By Energy conservation principle,
From equation (i)
12 = v₁ + 2v₂ ...(iii)
From equation (ii)

1	× 1 × 144 +	1	× 2 × 0 =	1	× 1 × v²₁ +	1	× 2 × v²₂
2		2		2		2

⇒ 144 = v²₁ + 2v²₂...(iv)
From equations (iii) and (iv)
144 = 144 + 4v²₂ - 48v₂ + 2²₂
⇒ 6v²₂ - 48v₂ = 0
⇒ 6v₂ (v₂ – 8) = 0
⇒ v₂ = 8 m/s