A large block of wood of mass M = 5 . 99kg is hanging from two long...

From energy conservation,

[after bullet gets embedded till the system comes momentarily at rest]

$\left(M + m\right)gh = \dfrac{1}{2}\left(M + m\right){v}_{1}^{2}$
[${v}_{1}$ is velocity after collision]

$∴ {v}_{1} = \sqrt{2\sigmah}$

Applying momentum conservation, (just before and just after collision)

$mv = \left(M + m\right){v}_{1}$

$v = \left(\dfrac{M + m}{m}\right){v}_{1} = \dfrac{6}{10 \times {10}^{- 3}} \times \sqrt{2 \times 9 . 8 \times 9 . 8 \times {10}^{- 2}}$

$\approx 831 . 55m{s}^{- 1}$