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 l/10th of its initial mass if its initial velocity is zero, (neglect gravity)

Explanation

`(dm)/(dt) = 50 kgs^(-1) , u=2 km s^(-1) = 2 xx 10^(3) ms^(-1)`
Initial velocity, `u_(0)=0`
(i) The thrust on the rocket.
`F =u(dm)/(dt) = 2 xx 10^(3) xx 50 = 1 xx 10^(5)` N
(ii) The velocity of the rocket.
`v=v_(0) + ulog_(e) m_(0)/m`
`=0+2 xx 10^(3) log_(e) [m_(0)/m_(0) xx 10] [therefore m=m_(0)/10]`
`=4.606 xx 10^(3) m//s`