Explain on the formula how it came to velocity

The kinetic energy of the combined mass immediately after the collision is converted into potential energy as it rises to height $h$.

$$\frac{1}{2} (m_b + m_p) V^2 = (m_b + m_p) g h$$

This cancels out the mass term from both sides, as it is present on both sides of the equation.

$$\frac{1}{2} V^2 = g h$$

This isolates $V^2$ on the left side.

$$V^2 = 2 g h$$

This gives the formula for the velocity $V$.

$$V = \sqrt{2 g h}$$