A 5 kg ball travelling East at 15 m/s hits a 10 kg ball moving at 5 m/s towards the West. After collision the 5 kg ball bounces back at 6m/s?

Take all vectors pointing East to be positive, and pointing West to be negative.

The small ball : m₁ = 5 kg, u₁ = 15 m/s, v₁ = -6 m/s
The big ball : m₂ = 10 kg, u₂ = -5 m/s, v₂ = ? m/s

According to the law of conservation of momentum :
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
5 × 15 + 10 × (-5) = 5 × (-6) + 10 × v₂
75 - 50 = -30 + 10v₂
10v₂ = 55
v₂ = 5.5 m/s

The speed of the big ball = 5.5 m/s
Direction : travelling East