A rocket has a mass of `2 xx10 ^(4)` kg of which half is fuel Assume that the fuel is consumed at a constant rate as the rocket is fired and there is contact thrust of `5 xx 10^(6)` N neglecting air resistance and any possible variation of g comput (i) the intial acceleration (ii) acceleration just when the whole fuel is consumed .

Explanation

Here, mass of rocket `m = 2xx 10^(4) kg`
mass of fuel `m = (1)/(2) (2xx10^(4)) kg = 10^(4) kg`
upthrust `= 5 xx 10^(6) N`
(i) Net force on the rocket
F = up thrust - weight (mg)
`5 xx 10^(6) -2xx 10^(4) xx 10`
` = 10^(5) (50 -2) = 48 xx 10^(5) `
`:.` Initial acceleration
`= (F)/(m) = (48xx 10^(5))/(2xx10^(4)) = 240 m//s^(2) `
When the fuel has been completly exhausted , remaining mass of rocket
F = upthrust - weight (m'' g)
`5 xx 10^(6) - 10^(4) xx 10 = 49 xx 10^(5) `
`:.` Acceleration = `(F)/(m) = (49 xx 10^(5))/(10^(4)) = 490 m//s^(2)` .