Question

A rocket, with an original mass of 20,000 kg, is launched vertically and expels 1000kg of mass every 20 seconds (take the average rocket recoil mass in applying momentum conservation). Determine the numerical value of the velocity of the rocket, after 2 10 second intervals, and also determine how far it has traveled at the end of that time.

Answer 1

Every second, the rocket expels 1000/20 kg = 50kg/sec

mass at any time will be m = 20000 - 50t

Change in momentum wrt time is

dm/dt × v

F = dm /dt × v

a = ( dm/dt × v) / m

dv/dt = 50v/m

dv/v = 50/(20000 -50t) × dt

Integrating we have

ln v = ln(1/400-t)

Put t = 20 sec and find out v,

For finding distance use a =vdv/ds and then you can calculate the integral.