a bullet moving with velocity of 100m/s pierces a block of wood and moves out with a velocity of 10m/s.if the thickness of the block reduces to one half of the previous value,what will be the emerging velocity of the bullet?

71.1 m/s

71.1 To find the emerging velocity of the bullet after the thickness of the block reduces, we can use the principle of conservation of momentum.

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Momentum is the product of mass and velocity, and it is a vector quantity.

Let's assign some variables:
- v1: initial velocity of the bullet (before hitting the block)
- v2: final velocity of the bullet (after passing through the block)
- m: the mass of the bullet
- M: the mass of the block
- t1: initial thickness of the block
- t2: final thickness of the block

Before the collision:
The momentum of the bullet before the collision is given by m * v1.
The momentum of the block before the collision is given by M * 0, since the block is stationary.

After the collision:
The momentum of the bullet after the collision is given by m * v2.
The momentum of the block after the collision is given by M * (v2 / t2), where (v2 / t2) represents the velocity of the block as the bullet passes through it.

Using the conservation of momentum principle, we can set up the equation:
m * v1 + M * 0 = m * v2 + M * (v2 / t2)

Since the block is stationary before and after the collision, we can simplify the equation:
m * v1 = m * v2 + M * (v2 / t2)

Now, we can solve for v2, the emerging velocity of the bullet after passing through the block.

Step 1: Rearrange the equation to isolate v2 on one side:
m * v2 + M * (v2 / t2) = m * v1

Step 2: Factor out v2 from the left side of the equation:
v2 * (m + M / t2) = m * v1

Step 3: Divide both sides of the equation by (m + M / t2) to solve for v2:
v2 = (m * v1) / (m + M / t2)

Now we have a formula to calculate the emerging velocity of the bullet after passing through a block with a reduced thickness.

To use this formula, substitute the given values:
- v1 = 100 m/s (initial velocity of the bullet)
- v2 = ? (emerging velocity of the bullet)
- t2 = t1 / 2 (final thickness of the block is one half of the previous value)

Substituting t2 into the formula:
v2 = (m * v1) / (m + M / (t1 / 2))

Finally, calculate v2 using the given variables and their values.