Question

A bullet of mass $7g$ is fired into a block weighing $7kg$ which is free to move. Calculate the initial velocity of a bullet if the velocity of the block with the bullet inside is $0.7m/s.$

Answer 1

Step 01: Given data:

The mass of block (M)$=7kg$
The initial velocity of the block $u_B=0m/s$ (since the block is at rest)
The mass of the bullet (m)$=7g=0.007kg(\sin ce1000g=1kg)$
Let the initial velocity of the bullet$=um/s$
The final velocity of the bullet and the box (v)$=0.7m/s$

Step 02:

According to the law of conservation of momentum, the momentum of a system must be conserved if no external force is acting.
Therefore initial momentum must be equal to final momentum.
$$\begin{gathered} p_{block}+p_{bullet}=p_{bullet+block}----equation\left(I\right) \\ Herep=momentum=mv \end{gathered}$$

Substituting the value of M, m, u, and v in equation (I) we get-

$$\begin{gathered} \left(7\right)\times \left(0\right)+(0.007)\times \left(u\right)=(7+0.007)\times (0.7) \\ 0.007u=4.90 \\ u=700m/s \end{gathered}$$

Hence the initial velocity of the bullet is equal to $700m/s.$