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 2 sec.
Answers
Answer:
The acceleration of rocket at 2 sec 0.526 m / s^2
Explanation :
According to the problem the mass of the rocket is ejected at a rate with the stated speed.
Therefore, let the momentum,= q
q can be calculated by multiplying the mass with the velocity
Now, change of momentum can be calculated from the force acting on a body
Let force= f
Therefore,f = dp / dt.
Thus, f = m × (dv / dt ) + v × ( dm / dt )
let the rocket is moving in a constant velocity
dv / dt = 0
Therefore,
f = v × ( dm / dt )
As the rate of ejection of mass ( dm / dt ) = 50 kg / s
and the speed is, v = 20 m / s
Therefore the force acting on the rocket
= 20 × 50
= 1000 N
Now, effective mass of the rocket after 2 s ( M )
= 2000 - 2 × 50
= 1900 kg
Therefore the acceleration of rocket at 2 sec is = f / m
= 1000 / 1900
= 0.526 m / s^2
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