Question

A rocket of mass 800 kg is launched from a
gravity free space . If rate of fuel
consumption is 300 kg/min and velocity of
exhaust gases is 20 m/s then the
acceleration of rocket after 1 minute will
be:-​

Answer 1

Explanation:

Relative velocity of exhaust gas V=2 km/s=2000 m/s

Thrust force F

t

=V

dt

dm

=2000×

dt

dm

Acceleration a=4.9 m/s

2

Mass of rocket M=1000 kg

Using Ma=F

t

−Mg

Or 1000×4.9=2000×

dt

dm

−1000×10

⟹

dt

dm

=7.35 kg/s

Answer 2

The  acceleration of rocket after 1 minute will  be 0.2 m/s²

Explanation:

Given:

Mass of the rocket M = 800 kg

Rate of fuel consumption dM/dt = -300 kg/min = -5 kg/s

Velocity of the exhaust gases v = 20 m/s

To find out:

The acceleration of rocket after 1 minute

Solution:

From the second law of Newton we know that

Force = Rate of change of momentum

$\implies F = \frac{d(Mv)}{dt}$

$\implies F=M\frac{dv}{dt}+v\frac{dM}{dt}$

If there is no external force acting then

F = 0

$\implies M\frac{dv}{dt}=-v\frac{dM}{dt}$

This is nothing but the thrust provided

Thus,

Thrust force

$F_t=M\frac{dv}{dt}=-v\frac{dM}{dt}$

$\implies F_t=-20\times (-5)$

$\implies F_t=100$ N

After 1 minute, the mass of the rocket will be

$m=800-300=500$ kg

If the acceleration after 1 minute is a then

$a=\frac{F_t}{m}$

$\implies a=\frac{100}{500}$

$\implies a=0.2$ m/s²

Hope this answer is helpful.

Know More:

Q: A rocket of initial mass 6000k.g eject mass at a constant rate of 16 k.g with constant relative speed of 11km/s. What is the acceleration of the rocket a minute after a blast?

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