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Q. A rocket of mass $4000kg$ is set for vertical firing. How much fuel must be consumed per second so that the rocket may have an initial upwards acceleration of magnitude $19.6ms^{- 2}$ . [Exhaust gases speed = $980ms^{- 1}$ ]

NTA AbhyasNTA Abhyas 2022

Solution:

$ma=u\frac{d m}{d t}-mg$
$\Rightarrow u\frac{d m}{d t}=m\left(a + g\right)$
$\Rightarrow \frac{d m}{d t}=\frac{4000 \times \left(19 . 6 + 9 . 8\right)}{980}$
$\frac{d m}{d t}=120kgs^{- 1}$