a bullet of mass 7g is fired into a block of wood weight 7kg the block is free to move after the impact , the velocity of the bullet and block is 17 cm/sec. what is the initial velocity of the bullet

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To find the initial velocity of the bullet, 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. In this case, let's denote the initial velocity of the bullet as v (unknown), the final velocity of the bullet and block as V (17 cm/sec), the mass of the bullet as m (7 g = 0.007 kg), and the mass of the block as M (7 kg).

Before the collision, the total momentum is given by the sum of the individual momentum of the bullet and the block:

Initial momentum = (mass of bullet) * (velocity of bullet) + (mass of block) * (initial velocity of block)

After the collision, the total momentum is given by the sum of the individual momentum of the bullet and the block:

Final momentum = (mass of bullet) * (velocity of bullet + velocity of block) + (mass of block) * (velocity of block)

Using the principle of conservation of momentum, we can equate the two equations:

(mv) + (M * 0) = (m * V) + (M * V)

Since the block is assumed to be at rest initially (velocity = 0), we can simplify the equation to:

mv = (m + M) * V

Now, we can substitute the known values:

(0.007 kg) * v = (0.007 kg + 7 kg) * (17 cm/sec)

Converting the units:

(0.007 kg) * v = (7.007 kg) * (0.17 m/sec)

Dividing both sides by 0.007 kg:

v ≈ (7.007 kg) * (0.17 m/sec) / 0.007 kg

v ≈ 119.69 m/sec

Therefore, the initial velocity of the bullet is approximately 119.69 m/sec.