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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) |
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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+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)` |
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