## To find the final speed of the first 4-kilogram mass, 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.

Before the collision, the first 4-kilogram mass has a speed of 6 m/s, so its momentum is:

Momentum = mass 脳 velocity

= 4 kg 脳 6 m/s

= 24 kg路m/s

The second 4-kilogram mass is initially at rest, so its momentum is zero.

After the head-on elastic collision, the momentum of the two masses is redistributed. However, since the system is isolated and no external forces are involved, the total momentum remains the same. Therefore, the total momentum after the collision is also 24 kg路m/s.

Now, let's consider the two masses that stick together after the collision.

Since both masses are identical and have the same mass of 4 kilograms, we can represent their combined mass as 8 kilograms.

Let the final speed of the two masses sticking together be v.

The momentum of the combined masses is equal to the product of the total mass and the final velocity:

Momentum = mass 脳 velocity

= 8 kg 脳 v

= 8v kg路m/s

According to the principle of conservation of momentum, the total momentum before the collision (24 kg路m/s) is equal to the total momentum after the collision (8v kg路m/s):

24 kg路m/s = 8v kg路m/s

Now, we can solve for v:

8v = 24

v = 24 / 8

v = 3 m/s

Therefore, the final speed of the first 4-kilogram mass is 3 m/s.

And the final speed of the two 4-kilogram masses that stick together is also 3 m/s.