Question

question no. 17 .....please tell early as soon as possible

Answer 1

 Rocket reaching a terminal constant velocity on its flight upwards...
 
  Let us apply conservation of momentum for rocket gases of mass dm separating from the rocket of mass m.  Given dm/dt = m/10 kg/sec.
 
  The mass dm has a relative velocity of  -1000 m/s wrt the current speed v of the rocket. The rocket moves forward with a relative velocity of +dv wrt current speed v of the rocket.

     So   - 1000 * dm + (m - dm) * dv = 0
               dv = 1000 dm / m
               dv/dt = (1000/m ) * dm/dt = 1000/m * m/10    (given)
               dv/dt = 100  m/s²
 
  We assume that in this process of thrust given by hot fast gases, acceleration due to gravity and air resistance do not affect it significantly.

Now there are gravity and air resistances opposing this thrust. So

      dv/dt = 100 - g - (0.15 * m * v)/m
              = 100 - 10 - 0.15 v
       dv/dt  = 90 - 0.15 v

For the rocket to reach a terminal velocity on its upward journey, dv/dt = 0.

        So    v = 90/0.15 = 600 m/sec.