Question

A bullet of mass a and velocity b is fired into a large block of wood of mass c, what is the final velocity of the system?

Answer 1

Step 1: Given

Mass of the bullet$=a$

Initial velocity of the bullet$=b$

Mass of the wood$=c$

Step 2: Determine the initial momentum

Let the initial momentum be $M_i$

$$\begin{gathered} M_i=mass\times initialvelocity \\ =ab \end{gathered}$$

Step 3: Determine the final momentum

Let the final velocity be $v$ and the final momentum be $M_f$

$$\begin{gathered} M_f=massofbulletinwood\times finalvelocity \\ =(a+c)v \end{gathered}$$

Here, both the mass of the bullet and the mass of wood are considered as the bullet enters the wooden block

Step 4: Determine the final velocity

According to the law of conservation of momentum, the initial momentum will be equal to the final momentum.

$$\begin{gathered} M_i=M_f \\ ab=(a+c)v \\ v=\frac{ab}{(a+c)} \end{gathered}$$

Therefore, the final velocity of the system is $v=\frac{ab}{(a+c)}$