To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, we can calculate the total momentum before the collision as follows:
Initial momentum = (mass of the first object × velocity of the first object) + (mass of the second object × velocity of the second object)
Initial momentum = (6 kg × 10 m/s) + (4 kg × 4 m/s) = 60 kg·m/s + 16 kg·m/s = 76 kg·m/s
Since the second object moves to the right with a final velocity of 10 m/s, its momentum after the collision can be calculated as:
Momentum of the second object after collision = mass of the second object × final velocity of the second object = 4 kg × 10 m/s = 40 kg·m/s
According to the conservation of momentum, the total momentum after the collision should be equal to the initial momentum. Therefore, the momentum of the first object after the collision can be calculated as:
Momentum of the first object after collision = Total initial momentum - Momentum of the second object after collision = 76 kg·m/s - 40 kg·m/s = 36 kg·m/s
Finally, we can calculate the velocity of the first object after the collision by dividing its momentum by its mass:
Velocity of the first object after collision = Momentum of the first object after collision / mass of the first object = 36 kg·m/s / 6 kg = 6 m/s
Therefore, the velocity of the first object after the collision is 6 m/s.