A rocket is fired vertically with a speed of 5 `kms^(-1)` from the earth's surface. How far from the earth does the rocket go before returning to the earth ? Mass of earth=`6.0xx10^(24)`kg, mean radius of the earth =`6.4xx10^(6)`m, G=`6.67xx10^(-11)Nm^(2)Kg^(-2).`

Explanation

Initial kinetic energy of rocket `=1//2mv^(2)=1//2xxmxx(5000)2=1.25xx10^(7)mJ`
At distance r from centre of earth, kinetic energy becomes zero
`therefore `Change in kinetic energy `=1.25xx10^(7)-0=1.25xx10^(7)mJ`
this energy changes into potential energy.
Initial potential energy at the surface of earth`=GM_(e)m//r`