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using energy conservation between initial and final position of pendulum after collision
KEi + PEi = KEf + PEf
PEi = 0
KEf = 0, at highest point velocity will be zero.
KEi = PEf
0.5*m1*V1^2 = m1*g*h
V1 = final speed of block just after collision = sqrt (2*g*h)
V1 = Vblock = sqrt (2*9.81*0.092) = 1.344 m/sec
Momentum of bullet-block system after collision will be:
Pf = m1*V1 + m2*V2
m2 = mass of bullet = 8 gm = 8*10^-3 kg
V2 = speed of bullet just after it exits the block = 180 m/sec
Pf = 1.2*1.344 + 8*10^-3*180 = 3.0528 kg-m/sec
Pf = 3.05 kg-m/sec = momentum of bullet-block system after the collision
Now using momentum conservation before and after collision
Since this completely inelastic collision, So
Pi = Pf
m1*u1 + m2*u2 = Pf
u1 = initial speed of block = 0 m/sec
u2 = Initial speed of bullet = ?
u2 = (Pf - m1*u1)/m2
u2 = (3.0528 - 1.2*0)/(8*10^-3)
u2 = 381.6 m/sec = Vbullet
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