How High Will the Block Rise After a Gunshot?

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When a bullet is fired vertically into a block of wood, the total momentum before the collision is calculated to be 4.41 kg·m/s. After the bullet embeds in the block, their combined mass moves upward at a velocity of 3.0964 m/s. To find the maximum height the block rises, one can use kinematic equations or conservation of energy, noting that energy is not conserved during the inelastic collision. The initial kinetic energy must be equated to the gravitational potential energy at the peak height. A miscalculation in energy conservation led to an incorrect height of 33.25 m, as energy is lost in inelastic collisions.
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A gun is fired vertically into a 1.4 kg block of wood at rest directly above it. If the bullet has a mass of 21g and speed of 210 m/s how high will the block rise into the air after the bullet becomes embedded in it?

the total momentum in the system is 210 x .021 = 4.41,
after the collision, the 1.421 mass is traveling upward at 3.0964 m/s... how would i find how high the mass rises into the air?
 
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y = y0 + v0t + ½at2
v = v0 + at
or energy conservation (it's conserved after the impact).
 
If one has a mass M, and it has an intial velocity V, it is a simple kinematics problem. For starters neglect air resistance.

If something is traveling vertical, it will be decelerating due to gravity.

Determine the equation that describes vertical motion in a gravity field.

Alternatively, use conservation of energy. The initial energy is kinetic. The mass travels vertically until it stops (vertical speed = 0). Equate initial kinetic energy with the change in gravitational potential energy.
 
Astronuc said:
If one has a mass M, and it has an intial velocity V, it is a simple kinematics problem. For starters neglect air resistance.
If something is traveling vertical, it will be decelerating due to gravity.
Determine the equation that describes vertical motion in a gravity field.
Alternatively, use conservation of energy. The initial energy is kinetic. The mass travels vertically until it stops (vertical speed = 0). Equate initial kinetic energy with the change in gravitational potential energy.

I got the right answer using kinematic equations (.491m) but i tried using conservation of energy and got a totally different answer:

KE initial = delta PE
1/2(0.021)(210)^2 = 1.421 (9.8) h
33.25 m = h
how am i setting up the equation wrong?
 
Energy is not conserved during the collision (unless the collision is elastic, which it isn't in this problem), see my first reply.
 
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