Fuel is consumed at the rats of `100kg//s` in a rocket The exhaust gases are ejected at a speed of `4.5 xx 10^(4) ms^(-1)` w.r.t the rocket What is the thrust experienced by the rocket Also calculate velocity of the rocket at the instant when its mass is reduced of rocket to be zero .

Answer

`4.5 xx 10^(6) N ; 1.036 xx 10^(5)ms^(-1)` .

Explanation

Here, `(dm)/(dt) = 100 kg//s, u = 4.5 xx 10^(4) ms^(-1)`
Thrust `F = u(dm)/(dt) = 4.5 xx 10^(4) xx 100`
`=4.5 xx 10^(6) N`
Also `upsilon = u log_(e) ((m_(0))/(m)) = 2.3026 u log_(10) ((m_(0))/(m))`
`upsilon = 2.3026 xx 4.5 xx 10^(4) log_(10) 10`
`=1.036 xx 10^(5) ms^(-1)` .