A rocket’s mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight can be obtained from Newton’ s law, and it is

 

where T is the rocket’s thrust and its mass as a function of time is given by m(t) = m₀(1 – rt/b). The rocket’s initial mass is m₀, the burn time is b, and r is the fraction of the total mass accounted for by the fuel.

Use the values T = 48,000 N, m₀ = 2200 kg, r = 0.8, g = 9.81 m/s², and b = 40 s. Determine the rocket’s velocity at burnout.

Transcribed Image Text:

dv m(t) = T - m(t)g dt