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The first & second stage of two stage ro...

The first & second stage of two stage rocket separately weigh 100 kg and 10 kg and contain 800kg and 90kg 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)

Text Solution

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`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`
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