Two objects move on a horizontal frictionless surface along the same line in the same direction which we shall refer to as foward direction. The trailing object of mass 2.0kg has a velocity of 15m/s foward. The leading object of mass 3.2 kg has avelocity of 11m/s foward. The trailing object catces up with the leading object and the two objects exprience a completely inelastic collision. what is the final velocity of the two objects

To find the final velocity of the two objects after the collision, we can use 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 (assuming no external forces are acting on the system).

The momentum of an object is calculated by multiplying its mass by its velocity: momentum = mass × velocity.

Let's calculate the total momentum before the collision:
Initial momentum of the trailing object (2.0 kg) = mass × velocity = 2.0 kg × 15 m/s = 30 kg·m/s.
Initial momentum of the leading object (3.2 kg) = mass × velocity = 3.2 kg × 11 m/s = 35.2 kg·m/s.

Now, since the collision is completely inelastic, the two objects stick together and move with a common final velocity (let's call it Vf).

So, after the collision, the total mass of the system will be the sum of the masses of the two objects: 2.0 kg + 3.2 kg = 5.2 kg.

Using the principle of conservation of momentum, we can set up the equation:
Initial momentum before collision = Final momentum after collision

(Initial momentum of the trailing object) + (Initial momentum of the leading object) = (Final momentum of the combined objects)

30 kg·m/s + 35.2 kg·m/s = 5.2 kg × Vf

Now, let's solve for Vf:

65.2 kg·m/s = 5.2 kg × Vf

Dividing both sides of the equation by 5.2 kg:
Vf = 65.2 kg·m/s / 5.2 kg

Vf = 12.54 m/s

Therefore, the final velocity of the combined objects after the collision is approximately 12.54 m/s.