A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 50.2 × 105 kg, of which 12.5 × 105 kg is fuel. The rocket engine is then fired for 450 s, during which fuel is consumed at the rate of 370 kg/s. The speed of the exhaust products relative to the rocket is 4.90 km/s. (a) What is the rocket's thrust? After the 450 s firing, what are (b) the mass and (c) the speed of the rocket?

165.2762 m/sec

Explanation:

The initial mass of the rocket and the fuel

M₀ = 5.02e6 kg

The initial mass of the fuel

Mf₀ = 1.25e6 kg

The rate of fuel consumption

dm/dt = 370 kg/sec

The duration of the rocket burn

Δt = 450 sec

The rocket exhaust speed

Ve = 4900 m/sec

The thrust, T

T = Ve (dm/dt) = 1813000 kg m/sec²

The mass of the expended propellant, ΔM

ΔM = Δt (dm/dt) = 166500 kg

The rocket's mass after the burn

M₁ = M₀ − ΔM = 4853500 kg

The speed of the rocket after the burn

Δv = Ve ln(M₀/M₁) = 165.2762 m/sec