The Conservation of Momentum Principle:
The conservation of momentum principle states that the total momentum of an isolated system remains constant if no external forces act on it.

Initial Conditions:
Let the initial velocity of the bullet be u. The bullet has a mass m and the block has a mass M. The bullet strikes the block and sticks to it. The block rises to a height h.

Applying the Conservation of Momentum Principle:
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of the bullet before the collision is given by:
Initial momentum of the bullet = mass of the bullet * initial velocity of the bullet
P₁ = mu

The momentum of the block before the collision is zero because it is initially at rest:
Initial momentum of the block = mass of the block * initial velocity of the block
P₂ = 0

The total momentum before the collision is:
Total initial momentum = P₁ + P₂ = mu

After the collision, the bullet and the block move together with a common velocity v. The total momentum after the collision is given by:
Total final momentum = (mass of the bullet + mass of the block) * final velocity of the bullet and block
= (m + M) * v

Equating the Initial and Final Momentum:
Since the total momentum before the collision is equal to the total momentum after the collision, we can equate the two expressions:

mu = (m + M) * v

Finding the Initial Velocity of the Bullet:
To find the initial velocity of the bullet (u), we rearrange the equation:

u = (m + M) * v / m

Conclusion:
The initial velocity of the bullet can be found using the equation u = (m + M) * v / m. By plugging in the known values for the masses (m and M) and the final velocity (v) of the bullet and block after the collision, we can calculate the initial velocity of the bullet.

(2gh) 1/2(m+M/m)