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). Aslo 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).

Fuel is consumed at the rate of 50 kg s^(-1) in a rocket. Find the thr

1.	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). Aslo 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).
Answer» Solution :`(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+xx10^(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)`.