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

To determine the emerging velocity of the bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after the interaction remains constant.

The momentum of an object can be calculated by multiplying its mass with its velocity. Since we are assuming the mass of the bullet remains constant, we can set up the following equation to represent the conservation of momentum:

Initial Momentum of the bullet = Final Momentum of the bullet

The initial momentum of the bullet can be calculated as mass of the bullet multiplied by the initial velocity:
Initial Momentum = mass × initial velocity

The final momentum of the bullet can be calculated as the mass of the bullet multiplied by the final velocity:
Final Momentum = mass × final velocity

Using the values provided in the question, we have:

Initial Momentum = mass × initial velocity = mass × 100 m/s
Final Momentum = mass × final velocity = mass × 10 m/s

Based on the conservation of momentum, the initial momentum should be equal to the final momentum:

mass × 100 m/s = mass × 10 m/s

We can cancel out the mass term from both sides:

100 m/s = 10 m/s

From this equation, we see that the mass term cancels out, meaning that the mass of the bullet is not required to determine the emerging velocity. The emerging velocity of the bullet will remain at 10 m/s.

Therefore, the emerging velocity of the bullet remains the same at 10 m/s, as the thickness of the block does not affect its velocity after piercing through the block.

work in the block=friction*distance

but friction force is mainly constant in the wood, so reducing the distance by 1/2 reduced the work absorbed by half

1/2 m 100^2 -1/2 m 10^2=friction work
so if friction work is halved, then that is added to the final KE.

final KE=1/2 m 10^2+1/2 (1/2 m 100^2-1/2 m 10^2)

final ke=1/2 m(10^2 + 1/2 10000 -1/2 100)

final ke=1/2m (50+5000)
1/2 m vf^2=1/2 m 5500
vf= sqrt 5500=75 m/s

check that work, I did it mostly in my head.