Answer to Question #3845 in Mechanics | Relativity for mia

Question

A 4.00 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?
(Ignore effects of gravity and air resistance.)

Answer 1

Let m₁ be the mass of the rocket, m₂ - the mass of burned fuel.
V₁ - velocity of the rocket after the fuel has burned,
V₂ - average velocity of burned fuel.
According to the law of conservation of linear momentum:


0 = m₁V₁ - m₂V₂


V₁ = V₂*m₂ / m₁
V₁ = 625*0.05/4 = 7.8125 m/s


So, the velocity of the rocket is 7.8 m/s.