Just before take-off, the mass of a rocket is 4000 kg and the velocity of ejection of the burnt fuel is 400 m`cdot s^(-1)` . What should be the rate of combustion of the fuel so that the rocket can take off vertically?

Explanation

Let the mass of gas ejected per second be m.
`therefore` Change of momentum of the ejected gas per second = mv = 400 m N.
`therefore` Force on the ejected gas = 400 m N = upward vertical reaction on the rocket.
Weight of the rocket = 400`xx 9.8`N.
For taking off, the vertical reaction force on the rocket must be slightly greater than the weight of the rocket.
As the limiting case, the vertical reaction force = weight of the rocket.
`therefore" " 400 m = 4000 xx 9.8 " " or, m = 98 "kg"cdot s^(-1)`.