Answer: 4 m/s
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a closed system remains constant before and after a collision.
Let's denote the initial velocity of the 2 kg ball as "v1i", the initial velocity of the 6 kg ball as "v2i", the final velocity of the 2 kg ball as "v1f", and the final velocity of the 6 kg ball as "v2f".
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
m1 * v1i + m2 * v2i = m1 * v1f + m2 * v2f
where m1 is the mass of the 2 kg ball, m2 is the mass of the 6 kg ball, v1i and v2i are the initial velocities, and v1f and v2f are the final velocities.
Given:
m1 = 2 kg
m2 = 6 kg
v1i = 12 m/s (initial velocity of the 2 kg ball)
v2i = 0 m/s (initial velocity of the 6 kg ball, as it is stationary)
v1f = 0 m/s (final velocity of the 2 kg ball, as it comes to rest)
Plugging in the given values into the conservation of momentum equation:
2 * 12 + 6 * 0 = 2 * 0 + 6 * v2f
24 = 6 * v2f
Dividing both sides by 6:
v2f = 24 / 6 = 4 m/s
So, the velocity of the 6 kg ball after the collision is 4 m/s.