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A rocket is fired vertically with a spee...

A rocket is fired vertically with a speed of `5kms^(-1)` From the Earth surface . How far from the Earth does the rocked go , before returning back ?

Text Solution

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Give, `M_(E) = 6.0xx10^(24)kg,R_(E)=6.4xx10^(6)m,`
`G=6.67xx10^(-11)Nm^(2)kg^(-2),v=5kms^(-1)`
We know that
`1/2mv^(2)-(GMm)/(R)=-(GMm)/(R+h)`
`:. (v^(2))/(2)=(GMh)/(R(R+H))" i.e.," (R+h)/(h)=(2GM)/(Rv^(2))=(2gR)/(v^(2))`
where , `2gR=11.2xx11.2xx10^(6):. (R+h)/(h)=(11.2xx11.2xx10^(6))/(25xx10^(6))=5.018`
`R=4.018h, :. h= (6.4xx10^(6))/(4.018)=1.593xx10^(6)m`
i.e., h = 1593 kM
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