Final answer:
In a perfectly elastic collision, the momentum and kinetic energy of the system are conserved. By using the conservation of momentum and the conservation of kinetic energy equations, we can solve for the final velocities of the balls. In this case, the final velocity of the white ball is 4 m/s.
Step-by-step explanation:
In a perfectly elastic collision, both the momentum and the kinetic energy of the system are conserved. Let's assume the white ball has a mass of 1 kg and the red ball has a mass of 2 kg. Since the red ball is at rest, its initial velocity is 0 m/s.
Using the law of conservation of momentum, we can calculate the final velocity of the white ball. The equation for the conservation of momentum is:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
Plugging in the values, we get:
(1 kg) * (2 m/s) + (2 kg) * (0 m/s) = (1 kg) * (v1_final) + (2 kg) * (v2_final)
Simplifying the equation, we get:
2 kg m/s = 1 kg * (v1_final) + 2 kg * (v2_final)
Since the collision is elastic, the kinetic energy is conserved. The equation for the conservation of kinetic energy is:
0.5 * m1 * (v1_initial)^2 + 0.5 * m2 * (v2_initial)^2 = 0.5 * m1 * (v1_final)^2 + 0.5 * m2 * (v2_final)^2
Plugging in the values, we get:
0.5 * (1 kg) * (2 m/s)^2 + 0.5 * (2 kg) * (0 m/s)^2 = 0.5 * (1 kg) * (v1_final)^2 + 0.5 * (2 kg) * (v2_final)^2
Simplifying the equation, we get:
2 J = 0.5 * (1 kg) * (v1_final)^2 + 0.5 * (2 kg) * (v2_final)^2
Now we have a system of equations that we can solve for the final velocities:
2 = v1_final + 2 * v2_final (from the conservation of momentum equation)
2 = 0.5 * (v1_final)^2 + v2_final^2 (from the conservation of kinetic energy equation)
Solving these equations will give us the final velocities of the two balls.
The final velocity of the white ball is 4 m/s.