A projectile is shot directly away from Earth\'s surface.Neglect the rotation of

Question

A projectile is shot directly away from Earth's surface.Neglect the rotation of the Earth. What multiple of Earth's radiusRE gives the radial distance (from the Earth'scenter) the projectile reaches if (a) its initialspeed is 0.207 of the escape speed from Earth and(b) its initial kinetic energy is 0.207 of thekinetic energy required to escape Earth? (Give your answers asunitless numbers.) I just cant figure out how to b... not quite sure A projectile is shot directly away from Earth's surface.Neglect the rotation of the Earth. What multiple of Earth's radiusRE gives the radial distance (from the Earth'scenter) the projectile reaches if (a) its initialspeed is 0.207 of the escape speed from Earth and(b) its initial kinetic energy is 0.207 of thekinetic energy required to escape Earth? (Give your answers asunitless numbers.) I just cant figure out how to b... not quite sure

Explanation / Answer

(a)

   from the theory the escape velocity is givenby
   vo = G M / 2 RE
   according to the law of conservation of energy weget
   (1/2) m vo2 - G Mm /RE = - G Mm / r
   from which we get
   r = 4 RE / 3
     = (4 / 3) RE
(b)
   the initial kinetic energy is given as
   KEi = (2 / 5) G Mm / 2RE
   deduce the multiple of RE  
(c)
   the mechanical energy is zero     

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