A body is projected vertically upwards from earth's surface. If velocity of projection is ( 3 1 ) rd of escape velocity, then the height upto which a body rises is ( R = radius of earth )

Question

A body is projected vertically upwards from earth's surface. If velocity of projection is ( 3 1 ​ ) rd of escape velocity, then the height upto which a body rises is ( R = radius of earth )

TestHub · Accepted Answer

V = 3 1 ​ R 2 GM ​ ​ TE At surface ​ = TE at height h ​ − R GM m ​ + 2 1 ​ m v 2 = − R + h GM m ​ + 0 − R GM m ​ + 2 1 ​ m 9 1 ​ × R 2 GM ​ = − R + h GM m ​ ( 9 1 ​ − 1 ) R GM m ​ = − R + h GM m ​ − 9 8 ​ R GM m ​ = − R + h GM m ​ 9 8 ​ R 1 ​ = R + h 1 ​ ⇒ 8 R + 8 h = 9 R 8 h = R ∴ h = 8 R ​

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