Initially before explosion, considering the bomb is at rest it’s velicity is zero.
i.e. u1=u2=0 m/s
When the bomb explodes into two pieces then:
Mass of one part (m1)= 3kg
Velocity of that part (v1)= 16m/s
Mass of another part (m2)= 6kg
Velocity of another part (v2)= ? (we require that to find its kinetic energy)
By the conservation of linear momentum:
m1 * u1 +m2 * u2 = m1 * v1 + m2 * v2
m1 * v1 + m2 * v2 = 0 (because u1 = u2 = 0)
m1 * v1 = -m2 * v2 ( negative sign shows that they have opposite direction)
So taking magnitude only:
m1 * v1 = m2 * v2
3 * 16 = 6 * v2
v2 = 8 m/s
Now, kinetic energy (KE2) = 1/2 (m2 *v2^2)
=0.5 * 6 * 8^2
= 3 * 64
=192 joules
Hence the KE of of 6kg mass is 192 joules