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 ]

Question

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 ] (A) 240kgs- 1 (B) 60kgs- 1 (C) 120kgs- 1 (D) None

Tardigrade Admin · Accepted Answer

ma=u(d m/d t)-mg ⇒ u(d m/d t)=m(a + g) ⇒ (d m/d t)=(4000 × (19 . 6 + 9 . 8)/980) (d m/d t)=120kgs- 1

Q. A rocket of mass $4000 k g$ 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 $19.6 m s^{- 2}$ . [Exhaust gases speed = $980 m s^{- 1}$ ]

$240 k g s^{- 1}$

$60 k g s^{- 1}$

$120 k g s^{- 1}$

None

$ma = u \frac{d m}{d t} - m g$
$\Rightarrow u \frac{d m}{d t} = m (a + g)$
$\Rightarrow \frac{d m}{d t} = \frac{4000 \times ( 19.6 + 9.8 )}{980}$
$\frac{d m}{d t} = 120 k g s^{- 1}$

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 ]

240kgs−1

60kgs−1

120kgs−1