To solve this question, 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. Therefore, the initial momentum of object A (m1) is (2 kg) * (3 m/s) = 6 kg·m/s, and the initial momentum of object B (m2) is (1 kg) * (4 m/s) = 4 kg·m/s.
Since the objects stick together after the collision, their final combined mass is the sum of their individual masses, which is 2 kg + 1 kg = 3 kg.
Let's assume the final velocity of the combined objects is v. According to the conservation of momentum, the total momentum after the collision is (3 kg) * (v m/s).
Setting the initial momentum equal to the final momentum, we have:
Initial Momentum = Final Momentum
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
Substituting the values into the equation, we get:
(6 kg·m/s) + (4 kg·m/s) = (3 kg) * v
Simplifying the equation:
10 kg·m/s = 3 kg * v
Dividing both sides of the equation by 3 kg:
v = 10 kg·m/s / 3 kg = 10/3 m/s ≈ 3.33 m/s
Therefore, the common velocity (v) after the collision is approximately 3.33 m/s.
Comparing this value with the given options, we can see that the correct answer is A) 2/3 m/s.