Question

a rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s the acceleration of the rocket 1 min after the blast is

Answer 1

Explanation:

Force on the rocket:

F= v dm/dt

= 12000 x 15= 180000 N

Mass after 1 min

M= m - dm/dt x t

= 5700 - 15 x 60

= 4800 kg

Accelration

a= F/m

or a= F-mg/M

= 180000 - (4800 x 10)/ 4800

=27.5 m/s2

Answer 2

Answer:

The acceleration of the rocket one minute after the blast is 27.5 m/s²

Explanation:

Given;-

     Mass of Rocket, M = 5700 kg

Rate of mass ejected, dm/dt = 15 kg/s

  Velocity of ejected mass, v = 12 km/s

                                      v = 12,000 m/s

      Time period, t = 60 s

Let the acceleration of rocket be 'a'.

Now, we know by formula that;-

  $Acceleration, \, a =[ \frac{v\frac{dm}{dt} }{M - \frac{dm}{dt}t } ]- g$

Putting the given values in the above formula, we get:-

           a = [ 12000 ×15 / 5700 - 15 × 60 ] - 10

           a = [ 180000 / 4800 ] - 10

           a = 37.5 - 10

           a = 27.5 m/s²

Hence, the acceleration of the rocket 1 min after the blast is 27.5 m/s²

Hope it helps! ;-))