A 3g bullet is fired horizontally into a 10kg block of wood

A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the bullet was:

Solution

speed of block before it start rise = sqrt ( 2gH) = sqrt (2*9.8*3*10^-3) = 0.2424 m/s

now momentum conservation

m1v1 = m1+m2)*V

=> 3*10^-3*V = 10*0.2424

=> v = 808 m/s speed of bullet