A rocket of initial mass `6000 kg` ejects gases at constant rate of `20 kg//s` with constant relative speed of `8 km//s`. What is the acceleration of the rocket after `100 s`.
(a) Neglect gravity , (b) include gravity and (c ) upward thrust.

Explanation

(a) `a = (v_(r))/(m) (dm)/(dt)`
`m = m_(0) - mu t = 6000 - 20 xx 100`
`= 4000 kg`
`v_(r) = 8 km//s = 8000 m//s`
`mu = (dm)/(dt) = 20 kg//s`
` = (8000)/(4000) xx 20 = 40 m//s^(2)`
(b) `a' = a - g = 40 - 10 = 30 m//s^(2)`
( c) Upward thrust `= v_(r ) (dm)/(dt) = 8000 xx 20 = N`
`= 1.6 xx 10^(5) N`