With what velocity must a body be thrown from earth's surface so that it may reach a maximum height of `4R_(e)` above the Earth's surface ? (Radius of the Earth `R_(e)=6400 km,g=9.8 ms^(-2)`).

Explanation

By using conservation of mechanical energy `(1)/(2)m_(0)`
`v_(2)-("GMm"_(0))/(R_(e))=0-("GMm"_(0))/((R_(e)+4R_(e)))`
`(1)/(2)m_(0)v^(2)=-("GMm"_(0))/(5R_(e))+("GMm"_(0))/("R"_(e))`
`implies(1)/(2)m_(0)v^(2)=(4)/(5)("GMm"_(0))/(R_(e))`
`impliesv^(2)=(8)/(5)("GM")/(R_(e))=(8)/(5)(gR_(e)^(2))/(R_(e))`
`v^(2)=(8)/(5)xx9.8xx6400xx10^(3)=10^(8)`
`impliesv=10" km"//"s".`