A rocket consumes `24kg` of fuel per second The burnt gases escape the rocket at a speed of `6.4km//s` relative to the rocket Calculate the upthrust recevied by the rocket Also calculate the velocity acquired by the rocket when the mass redues to `1//100th` of its initial mass.

Answer

`1.536 xx10^(5) N; 2.984 xx10^(4) m//s` .

Explanation

Here,` (dm)/(dt) = 24 kg//s`
`u = 6.4 km//s = 6.4 xx 10^(3) m//s`
upthrust ` = u ((dm)/(dt)) = 6.4 xx 10^(3) xx24`
`=1.536 xx 10^(5)N`
As `upsilon = u log_(e) (m_(0)/(m))`
`:. Upsilon = 6.4 xx 10^(3) log_(e) ((m_(0))/(m_(0) //100))`
`= 64 xx 10^(3) xx 2.303 log_(10) (100)`
`upsilon = 6.4 xx 10^(3) xx 2.303 xx 2`
`2.948 xx 10^(4) m//s` .