Question

In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of $2400\,\,m{{s}^{-1}}$ . The acceleration of the rocket is:

• A. $19.6\,m{{s}^{-2}}$
• B. $30.2\,m{{s}^{-2}}$
• C. $40\,m{{s}^{-2}}$
• D. $49.8\,\,m{{s}^{-2}}$

Answer 1

Answer: (C)

$40\,m{{s}^{-2}}$

Answer 2

Thrust force on the rocket
$F_{t}=v_{r}\left(-\frac{d m}{d t}\right)$
or $m a=v_{r}\left(-\frac{d m}{d t}\right)$
where $v_{r}$ is the exhaust velocity of gases and
$-\frac{d m}{d t}$ is the mass of the ejected per unit time.
Given, $v_{r}=2400\,ms ^{-1},-\frac{d m}{d t}=\frac{1}{60} kg / s$
$m=1\, kg$
Substituting the values in above relation
$1 \times a =2400 \times \frac{1}{60}$
or $a =40 \,ms ^{-2}$