linear momentum

[7tongc5]

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 travelling upward at 3.0964 m/s... how would i find how high the mass rises into the air?

[Päällikkö]

y = y0 + v0t + ½at2
v = v0 + at
or energy conservation (it's conserved after the impact).

[Astronuc]

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.

[7tongc5]

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?

[Päällikkö]

Energy is not conserved during the collision (unless the collision is elastic, which it isn't in this problem), see my first reply.