Question

6.
A rocket of mass 2000 kg is ejecting the gases
at the rate of 50 kg/sec with speed of 20 m/sec
in gravity free space. Find the acceleration of
rocket at 4 sec.
​

Answer 1

$\huge{ \underline{ \underline{ \sf{ ANSWER - }}}}$

▶We have momentum of rocket at time t= change in momentum of rocket at time t (because initial momentum is zero) = mass of rocket at time t × velocity of rocket at time t

= (2000 - 50t) × v

▶Now I think by conservation of momentum of an isolated system, I'll be able to figure out v in terms of t.

▶So, 0 (which is the initial momentum of rocket before it started releasing gases) = (2000 - 50t)v - 50t × (20), (which is the final momentum of rocket + gases system.)

By this, we have

v = (50t × 20)/(2000 - 50t)

Thus,

momentum = (2000 - 50t)v = 1000t

▶Now differentiate it w.r.t. time and we got

dp/dt = 1000

▶Thus force = mass × acceleration = 1000

▶acceleration = 1000/(2000 - 50t), but t is equal to 2 as given.

Therefore

acceleration = 1000/(2000 - 50×2)

= 1000/1900

= 10/19 m/s^2

Answer 2

Explanation:

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