First slide

Second law

Question

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 $m s^{- 1}$ . To give an initial upward
acceleration of 20 $m s^{- 2}$ , the amount of gas ejected per second to supply the needed thrust will be (Take,
9 = 10 $m s^{- 2}$ )

Moderate

A

127.5 $k g s^{- 1}$
B

187.5 $k g s^{- 1}$
C

185.5 $k g s^{- 1}$
D

137.5 $k g s^{- 1}$

Solution

$F = u \frac{d m}{d t} = m (g + a)$
$\Rightarrow \frac{d m}{d t} = \frac{m (g + a)}{u} = \frac{5000 \times (10 + 20)}{800} = 187.5 {kgs}^{- 1}$

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