To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the total momentum is given by:
Total momentum before = (mass1 * velocity1) + (mass2 * velocity2)
After the collision, the two masses stick together, so we have a combined mass of 2m + m = 3m. Let's denote the final velocity of the combined masses as Vf.
The total momentum after the collision is:
Total momentum after = (combined mass) * Vf
Setting the total momentum before and after the collision equal, we can write the equation:
(mass1 * velocity1) + (mass2 * velocity2) = (combined mass) * Vf
Substituting the given values:
(2m * 2v) + (m * v) = (3m) * Vf
Simplifying:
4mv + mv = 3mVf
5mv = 3mVf
Dividing both sides by 3m:
5v = Vf
Therefore, after the collision, the combined masses will have a velocity of 5v.