Final answer:
The speed of the 10 kg shark after swallowing a 0.5 kg fish that was at rest is approximately 4.76 m/s, calculated using the conservation of momentum.
Step-by-step explanation:
The scenario described concerns a 10 kg shark that swallows a 0.5 kg fish. The principle involved here is the conservation of momentum, which states that within a closed system, the total momentum before an event must equal the total momentum after, assuming no external forces act on the system. In this case, we can consider the shark and the fish a closed system. Before the shark swallows the fish, the total momentum is the sum of the momentum of the shark and the fish. The shark's momentum is 10 kg × 5 m/s = 50 kg·m/s, and the fish's momentum is 0 kg·m/s because it is at rest.
After the shark eats the fish, their combined mass is 10.5 kg. To find the final speed of the shark after eating the fish, we set the total initial momentum equal to the total final momentum (since momentum is conserved) and solve for the final speed. This gives us:
Total final momentum = (10 kg + 0.5 kg) × final speed
50 kg·m/s = 10.5 kg × final speed
final speed = 50 kg·m/s / 10.5 kg
final speed = 4.76 m/s
The speed of the large fish after eating the smaller fish is therefore approximately 4.76 m/s.