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A body is projected vertically from the earth`s surface with velocity equal to half of the escape velocity.what is maximum height reached by the body?

A body is projected vertically from the earth`s surface with velocity equal to half of the escape velocity.what is maximum height reached by the body?

Grade:11

2 Answers

Arun
25750 Points
6 years ago
From conservation of mechanical energy
(1/2)* m(Ve/2)^2 = mgh/[1+(h/r)]
As Ve = \sqrt(2gR), where R = radius of earth
Hence
(1/2)*m.(\sqrt2gR/2)^2 = m*g *h*R /(h+R)
On solving h = R/3
Vikram
13 Points
5 years ago
from law of conservation of energy
  (1/2)mv^2 = mgh
   (1/2)v^2 = gh
   h = (1/2g)v^2
  putting v= (under root 2gr)/2
   h=  2gr/4×2g
   h= r/4
  h= (radius of earth)/4
   

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