A 9.0 kg shell at rest bursts into two pieces of 3.0 kg and 6.0 kg…

Step 1. (a) $3.0\ \text{kg} \times 16\ \text{m/s} + 6.0\ \text{kg} \times v = 0$, so $v = -8.0\ \text{m/s}$: $8.0\ \text{m/s}$ the opposite way.

Step 2. (b) $\tfrac12 \times 3.0\ \text{kg} \times (16\ \text{m/s})^2 + \tfrac12 \times 6.0\ \text{kg} \times (8.0\ \text{m/s})^2 = 384\ \text{J} + 192\ \text{J} = 576\ \text{J}$.