To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant before and after a collision.
The momentum of an object is defined as the product of its mass and velocity: momentum = mass × velocity.
Let's denote the mass of the first ball as m₁ (0.2 kg), its initial velocity as v₁ (3 m/s), the mass of the second ball as m₂ (0.5 kg), and its final velocity as v₂ (1 m/s).
Before the collision, the total momentum is given by: Initial momentum = (mass of the first ball × velocity of the first ball) + (mass of the second ball × velocity of the second ball) m₁v₁ + m₂v₂ = (0.2 kg × 3 m/s) + (0.5 kg × 0 m/s) m₁v₁ + m₂v₂ = 0.6 kg·m/s
After the collision, the total momentum is also conserved: Final momentum = (mass of the first ball × final velocity of the first ball) + (mass of the second ball × final velocity of the second ball) m₁v₁' + m₂v₂' = (0.2 kg × ? m/s) + (0.5 kg × 1 m/s) m₁v₁' + m₂v₂' = ? kg·m/s + 0.5 kg·m/s m₁v₁' + m₂v₂' = ? kg·m/s + 0.5 kg·m/s
Since we know that the second ball moves to the right with a velocity of 1 m/s after the collision (v₂' = 1 m/s), we can substitute the values into the equation:
0.2 kg × ? m/s + 0.5 kg × 1 m/s = 0.6 kg·m/s
Simplifying the equation:
0.2 kg × ? m/s + 0.5 kg = 0.6 kg
Subtracting 0.5 kg from both sides:
0.2 kg × ? m/s = 0.6 kg - 0.5 kg 0.2 kg × ? m/s = 0.1 kg
Dividing both sides by 0.2 kg:
? m/s = 0.1 kg / 0.2 kg ? m/s = 0.5 m/s
Therefore, the speed of the first ball after the collision is 0.5 m/s.