A rocket of mass 6000kg is fired from earth with speed $1 k m s^{- 1}$ . What should be the rate of ejection of gas, so that it moves with acceleration of $20 m / s^{2}$ . Take $g = 10 m / s^{2}$

Question

Verified by Toppr

Answer 1

For the rocket to move with acceleration $a$ , thrust required is -

$F = m (a + g)$ ...(1)

To provide this thrust, let dm/dt be rate of ejection of gas.

$F = v (\frac{d m}{d t})$ ...(2)

From (1) & (2),

$m (a + g) = v (\frac{d m}{d t})$

$\frac{d m}{d t} = \frac{m ( a + g )}{v}$

$\frac{d m}{d t} = \frac{6 0 0 0 \times ( 2 0 + 1 0 )}{1 0 0 0}$

$\frac{d m}{d t} = 180 k g / s$

Therefore, rate of ejection of gas should be $180 k g / s$ .

Answer 2

For the rocket to move with acceleration

a

, thrust required is -

F = m (a + g)

...(1)

To provide this thrust, let dm/dt be rate of ejection of gas.

F = v (\frac{d m}{d t})

...(2)

From (1) & (2),

m (a + g) = v (\frac{d m}{d t})

\frac{d m}{d t} = \frac{m ( a + g )}{v}

\frac{d m}{d t} = \frac{6 0 0 0 \times ( 2 0 + 1 0 )}{1 0 0 0}

\frac{d m}{d t} = 180 k g / s

Therefore, rate of ejection of gas should be

180 k g / s

.