A rocket burns 0.5 kg of fuel per second ejecting it as gases with a velocity of `1600 m//s` relative to the rocket . How much force is exerted on the rocket ? Also , calculate the velocity attainted by the rocket , when its mass
reduces to `(1)/(200)` th of its initial mass .

Explanation

Here , ` (dm)/(dt) = - 0.5 kg // s, u = 1600 m // s `
` F= ? upsilon = ?`
`m = (1)/(200) m_(0) `
` F = -u ((dm)/(dt)) = - 1600 (-0.5 ) = 800 N `
As `upsilon = 2.303 u log_(10) ((m_(0))/(m)) `
` = 2.303 xx 1600 log_(10) 200 `
` = 2.303 xx 1600 xx 2.3010 `
` = 8478.7 m//s `
` 8 . 48 km // s` .