Question
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?
Answers
Damon
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
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