The first & second stage of two stage rocket separately weigh 100 kg and 10 kg and contain 800 kg and 90 kg fuel respectively. If the exhaust velocity of gases is 2 km/sec then find velocity of rocket (nearly) (log_(10)5=0.6990) (neglect gravity).

The first & second stage of two stage rocket separately weigh 100 kg a

1.	The first & second stage of two stage rocket separately weigh 100 kg and 10 kg and contain 800 kg and 90 kg fuel respectively. If the exhaust velocity of gases is 2 km/sec then find velocity of rocket (nearly) (log_(10)5=0.6990) (neglect gravity).
Answer» Solution :`V=V_(0)+2.3 U LOG (m_(0)//m)` Velocity as the first stage is detached `= V_(0)` `V_(0)=2.3 ulog(m_(0)//m)` `= 2.3xx2xx10^(3)xxlog (1000//200)` `= 2.3xx2xx0.699xx10^(3)=3.2xx10^(3)` Velocity ACQUIRED with second stage = V `V=V_(0)+2.3u log(m_(0)//m)` `= 3.2xx10^(3)+2.3xx2xx10^(3)xxlog(100//10)` `= 3.2xx10^(3)+4.6xx10^(3)=7.8xx10^(3)m//s`