Do I use kinetic energy or momentum to figure out the final velocity? [duplicate]

Question

Let's say hypothetically that a gun fires a bullet which has a mass of 1 gram and a $V_\mathrm{initial}$ of 10 m/s, which becomes lodged in a wooden block that has a mass of 9 grams and is initially at rest. The impact causes the block (with the lodged bullet) to travel at a velocity $V_\mathrm{final}$. What is $V_\mathrm{final}$?

I'm confused. I don't know whether I should use momentum or kinetic energy to figure out the $V_\mathrm{final}$. I plugged in the numbers to both equations, and the resulting values of $V_\mathrm{final}$ didn't agree.

Answer 1

Okay, lets start this off with a simple answer, you can solve it many ways using fundamental algebra, that includes work energy, kinematic-dynamic and Impulse momentum theorem. I personally check myself with both. We can go into more detail later if we need so.

I personally use Work-energy-kinematic ways. However, we can start however by using Impulse-momentum theorem, just to make this short

Fnet * t = m * (change in) Velocity.

now, we can just say that the impulse that will produced on impact is 0.01 Ns the impact will result in mass combined of 0.01kg's, thus 0.01Ns/0.01kg is 1 m/s resultant velocity.

We however, can use energy to find velocity after v=(square root) 2(KE)/mass

Answer 2

You can think of the problem this way: You can just divide the velocity by mf/mi or (9+1)/1, or 10/1, which is the same as multiplying the initial velocity by 1/10, which is the amount of mass that the motion energy is changing to apply to, which gives 1 m/s final velocity.