A body is projected vertically from the surface of the earth of radius rr with a velocity equal to half of the escape velocity. the maximum height reached by the body is:
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v= √ 2gh
Velocity (escape ) = √ 2 G M / R
v = 1/2 Velocity ( escape ) -------- ( Given )
that's why
1/2 × √ 2 G M / R = √ 2gh
GM/ 4 R = g h
h= GM / 4Rg
h = max . Height reached by body
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