Physics

To find the initial velocity of the second object, we will use the principle of conservation of momentum and the relationship between the kinetic energy before and after the collision.

 

Let the initial velocity of the second object be .

The initial momentum of the system is .

After the inelastic collision, the two objects stick together, so the combined mass is .

Let the velocity of the combined objects after the collision be .

By conservation of momentum, . So .

 

Calculate the initial kinetic energy of the system:

The initial kinetic energy .

 

Calculate the final kinetic energy of the system after the collision:

The final kinetic energy .

Substitute into , we get .

 

The loss in kinetic energy is given by .

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