Fuel is consumed at the rate of `50 kg s^(-1)` in a rocket. Find the thrust on the rocket if the velocity of the exhaust gases is `2 km s^(-1)`. Also calculate the velocity of the rocket at the instant, when its mass is reduced to 1/10th of its initial mass if its initial velocity is zero. (neglect gravity)

Explanation

`(dm)/(dt)=50 kgs^(-1) , u=2 km s^(-1)=2xx10^(3)ms^(-1)`,
initial velocity, `u_(0)=0`
(i) The thrust on the rocket,
`F=u(dm)/(dt)=2xx10^(3)xx50=1xx10^(5)N`.
(ii) The velocity of the rocket,
`v=v_(0)+u "log"_(e )(m_(0))/(m)`
`=0+2xx10^(3)log_(e )((m_(0))/(m_(0))xx10) " " (because m = (m_(0))/(10))`
`=2xx10^(3)log_(e )10=2xx10^(3)xx2.303 log_(10)10`
`=4.606xx10^(3)(m)/(s)`