Question

5. A 4.0 kg model rocket is launched, shooting 50.0 g of burned fuel from its exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned?

Answer 1

To find the velocity of the rocket after the fuel has burned, we need to use the conservation of momentum principle. The principle states that the momentum of an isolated system (in this case, the rocket and the expelled fuel) is constant, meaning that the initial momentum of the system is equal to the final momentum of the system.

The initial momentum of the system is the momentum of the rocket before the fuel is expelled, which is given by:

p_initial = m_rocket * v_initial = 4.0 kg * 0 m/s = 0 kg m/s

The final momentum of the system is the momentum of the rocket after the fuel is expelled, which is given by:

p_final = m_rocket * v_final

The momentum of the expelled fuel is given by:

p_fuel = m_fuel * v_exhaust = 0.05 kg * 625 m/s = 31.25 kg m/s

The total momentum of the final system is the sum of the rocket and the expelled fuel.

p_total = p_rocket + p_fuel

Now we can use conservation of momentum equation

p_initial = p_final

0 = m_rocket * v_final + m_fuel * v_exhaust

Now we can solve for v_final

v_final = (p_initial - p_fuel) / m_rocket

v_final = (0 - 31.25 kg m/s) / 4.0 kg = -7.8125 m/s

So the final velocity of the rocket after the fuel is expelled is -7.8125 m/s, which means that the rocket is moving in the opposite direction of the expelled fuel.