How to Calculate Muzzle Speed in an Inelastic Collision?

[AeroFunk]

A 16 g bullet strikes and becomes embedded in a 1.30 kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.22, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?

Is there anthor equation i can use besides the conservation of momentum
mv=(m+M)v' I can't use conservation of energy because its inelastic right? So what can I do help please.

 

[Pyrrhus]

Kinematic:

$$v^2 = v_{o}^2 + 2a \Delta x$$

and Newton's 2nd Law to get the acceleration

$$\sum_{i=1}^{n} \vec{F}_{i} = m \vec{a}$$

 

[lurflurf]

I can't use conservation of energy because its inelastic right? So what can I do help please.

You can't use conservation of kinetic energy.
Use can use conservation of energy.

 

[arildno]

A 16 g bullet strikes and becomes embedded in a 1.30 kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.22, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?

Is there anthor equation i can use besides the conservation of momentum
mv=(m+M)v' I can't use conservation of energy because its inelastic right? So what can I do help please.

Split your problem in two:
1. Assume that after the collision is finished, the system begins moving with some velocity $$v_{0}$$
Determine $$v_{0}$$ with Cyclovenom's first equation.
2. You may now use momentum conservation during the collision phase to determine the muzzle speed (assuming the bullet did not meet any air resistance in the phase between it is shot out until the collision begins)