Question

A rocket of mass $5700kg$ ejects mass at a constant rate of $15kg/s$ with constant speed of $12km/s$. The acceleration of the rocket $1minute$ after the blast is $(g=10m/s^2)$

• A. $34.9m/s^2$
• B. $27.5m/s^2$
• C. $3.50m/s^2$
• D. $13.5m/s^2$

Answer 1

The correct option is B $27.5m/s^2$

Force on the rocket

$F=\frac{vdm}{dt}$

$=12000\times 15=180000N$

Mass after one min

$M=m-\frac{dm}{dt}\times t$

$=5700-15\times 60$

$=4800kg$

Acceleration ,$a=\frac{F}{M}$

or

$=\frac{F-mg}{M}$

$=\frac{180000-(4800\times 10)}{4800}$

$=27.5m/s^2$

Hence (B) Option is correct