When bullet meets pendulum

A pendulum consisting of a bob of mass $M$ is suspended by a rigid rod of length $L$ . A bullet having the same mass as the bob and velocity $v$ impacts the bob at an angle as shown in the figure and stays embedded in it. After the impact, the bob reaches a maximum angular displacement of $\theta$ . Find the value of initial velocity $v$ of the bullet in $\text{ms}^{-1}$ .

Details and Assumptions:

• Mass of the rod is negligible.

• $M = 39 \text{ kg}$ .

• $\theta = 60^{\circ}$ .

• $x = 30^{\circ}$ .

• $L = 30 \text{ m}$ .

• Take $g = 10 \text{ ms}^{-2}$ .