Answer:
The 5 kg ball moves 3.78 m/s to the left, and the 4 kg ball moves 7.22 m/s to the right.
Explanation:
Momentum before = momentum after
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
(5 kg) (6 m/s) + (4 kg) (-5 m/s) = (5 kg) v₁ + (4 kg) v₂
10 m/s = 5 v₁ + 4 v₂
Assuming an elastic collision, kinetic energy is conserved.
½ m₁ u₁² + ½ m₂ u₂² = ½ m₁ v₁² + ½ m₂ v₂²
m₁ u₁² + m₂ u₂² = m₁ v₁² + m₂ v₂²
(5 kg) (6 m/s)² + (4 kg) (-5 m/s)² = (5 kg) v₁² + (4 kg) v₂²
280 m²/s² = 5 v₁² + 4 v₂²
Substituting:
v₂ = (10 − 5 v₁) / 4
280 = 5 v₁² + 4 [(10 − 5 v₁) / 4]²
280 = 5 v₁² + (10 − 5 v₁)² / 4
1120 = 20 v₁² + (10 − 5 v₁)²
1120 = 20 v₁² + 100 − 100 v₁ + 25 v₁²
0 = 45 v₁² − 100 v₁ − 1020
0 = 9 v₁² − 20 v₁ − 204
0 = (9 v₁ + 34) (v₁ − 6)
v₁ = -3.78 m/s or 6 m/s
u₁ = 6 m/s, so v₁ = -3.78 m/s. Solving for v₂:
v₂ = (10 − 5 v₁) / 4
v₂ = 7.22 m/s
The 5 kg ball moves 3.78 m/s to the left, and the 4 kg ball moves 7.22 m/s to the right.
