A rocket of mass 50 kg is launched vertically. Its fuel is being burnt at a rate of 2 kg s-1 and its exhaust gas is being forced out with a speed of 1000 m s-1. What is the initial acceleration of the rocket?

1 answer

mv rocket = m v exhaust

so

d/dt (mv rocket) = d/dt (mv exhaust)

m v rocket = (50 - 2 t)v = m v exhaust = (2t)1000

50 v - 2vt = 2000 t

50 dv/dt -2v - 2t dv/dt = 2000

at t = 0 and v = 0

50 dv/dt = 50 a = 2000

a = 40 m/s^2