A rocket of mass 1000kg containing a propellant gas of 3000kg is to be launched vertically.If the fuel is consumed at a steady rate of 60kg/s.Calculate the least velocith of the exhaust gases if the rocket and the content will just lift off the launching pad immediately after firing?


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Question Number 49491 by Necxx last updated on 07/Dec/18

$A r o c k e t o f m a s s 1000 k g c o n t a i n i n g$ $a p r o p e l l a n t g a s o f 3000 k g i s t o$ $b e l a u n c h e d v e r t i c a l l y . I f t h e f u e l$ $i s c o n s u m e d a t a s t e a d y r a t e o f$ $60 k g / s . C a l c u l a t e t h e l e a s t v e l o c i t h$ $o f t h e e x h a u s t g a s e s i f t h e r o c k e t$ $a n d t h e c o n t e n t w i l l j u s t l i f t o f f$ $t h e l a u n c h i n g p a d i m m e d i a t e l y$ $a f t e r f i r i n g ?$
	Answered by ajfour last updated on 07/Dec/18

	$\frac{M d v}{d t} = (v_{e x h a u s t}) \frac{d M}{d t} - M g$ $t o j u s t l i f t o f f \frac{d v}{d t} = 0$ $\Rightarrow v_{e x h a u s t} = \frac{M g}{(d M / d t)}$ $= \frac{4000 \times 9.8}{60} m / s .$ $= \frac{40 \times 98}{6} = \frac{3920}{6} = 653.3 \frac{m}{s} .$
	Commented by Necxx last updated on 07/Dec/18

	$p l e a s e c a n y o u e x p a n t i a t e m o r e o n$ $w h a t b r o u g h t a b o u t t h e f o r m u l a$ $y o u u s e d .$ $T h a n k s f o r h e l p i n g m r . A j f o u r$
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