Question

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

• A. $127.5 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$
• B. $187.5 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$
• C. $185.5 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$
• D. $137.5 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$

Answer 1

Answer: (B)

$187.5 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$

Answer 2

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

⇒ $\frac { d m } { d t } = \frac { m ( g + a ) } { u }$ $= \frac { 5000 \times ( 10 + 20 ) } { 800 }$ $= 187.5 \mathrm {~kg} / \mathrm { s }$