Final answer:
The unknown speed of the other part of the rocket, after conservation of momentum is applied, is found to be 350 m/s.
Step-by-step explanation:
The problem given can be solved using the law of conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act upon it. The two fragments resulting from the explosion of the rocket must have combined momenta that equal the original momentum of the rocket before the explosion.
The initial momentum (Pi) of the rocket is the product of its mass (m) and its velocity (v):
Pi = m × v
For the rocket with an initial mass of 5.0 kg traveling at 200 m/s:
Pi = (5.0 kg) × (200 m/s) = 1000 kg·m/s
After the explosion, we have two parts. Part 1, with a mass of 3.0 kg, has a momentum of:
P1 = (3.0 kg) × (100 m/s) = 300 kg·m/s
The remaining piece (Part 2) must have a momentum that, when added to P1, equals Pi. Let's call the mass of Part 2 m2 (which is 5.0 kg - 3.0 kg = 2.0 kg), and its unknown velocity v2. The momentum of Part 2:
P2 = m2 × v2
P2 = (2.0 kg) × v2
According to the law of conservation of momentum:
Pi = P1 + P2
1000 kg·m/s = 300 kg·m/s + (2.0 kg) × v2
Now we can solve for v2:
700 kg·m/s = (2.0 kg) × v2
v2 = 350 m/s
The unknown velocity of the other part of the rocket is 350 m/s.