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{\bf Question}

A rocket has an initial mass of $7\times 10^4$kg and on firing
burns its fuel at a rate $250$kgs$^{-1}$.  The exhaust velocity is
$2.5\times 10^3$ms$^{-1}$.  If the rocket has a vertical ascent
from resting on the earth, how long after the rocket engines fire
will the rocket take off.  What is wrong with the design of this
rocket?

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{\bf Answer}

The rocket will lift off when the thrust just exceeds its weight.

$\ds {\rm Thrust} = u\alpha$

$\ds {\rm Weight} = mg = (m_0 - \alpha t)g$

Therefore $\ds u \alpha = (m_0 - \alpha t)g \Rightarrow t =
\frac{m_0}{\alpha} - \frac{u}{g}$

Thus using the data in the question it will lift off at 25 seconds
after ignition.

The design problem is that there is too much fuel on board.




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