Final answer:
The velocity of the model rocket after expelling fuel is calculated using the conservation of momentum principle, resulting in a velocity of 7.81 m/s in the direction opposite to the expelled fuel.
Step-by-step explanation:
The question asks about the velocity of a 4 kg model rocket after expelling 50.0 g of burned fuel at an average velocity of 625 m/s. To find the final velocity of the rocket, we can use the conservation of momentum principle. The momentum of the system (rocket plus fuel) before and after the fuel expulsion must remain constant because no external forces are involved.
Initially, the rocket is at rest, so the initial momentum is zero. After the fuel is burned and expelled, the momentum of the fuel and rocket must still add up to zero (since the initial momentum was zero). The formula for conservation of momentum in this case is:
mrocket × vrocket + mfuel × vfuel = 0
Where mrocket is the mass of the rocket, vrocket is the velocity of the rocket, mfuel is the mass of the fuel, and vfuel is the velocity of the fuel.
By plugging in the known masses and the velocity of the fuel, we can solve for the velocity of the rocket:
(4 kg) × vrocket + (0.050 kg) × (-625 m/s) = 0
vrocket = - (0.050 kg × 625 m/s) / 4 kg
vrocket = - (31.25 m/s) / 4 kg
vrocket = -7.81 m/s
The minus sign indicates that the rocket moves in the opposite direction to the expelled fuel. Therefore, the velocity of the rocket after the fuel has burned is 7.81 m/s in the direction opposite to the expelled fuel.