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A particle is thrown with escape velocity v from the surface of Earth calculate its velocity at height 3R

A particle is thrown with escape velocity v from the surface of Earth calculate its velocity at height 3R

Grade:11

2 Answers

Arun
25750 Points
6 years ago
Dear Raja
 
V = sqrt (GM/2R)
 V = escape velocity/2
V = 11.2/2
V = 5.6 km/sec
 
 
Regards
Arun (askIITians forum expert)
Sunder Muthukumaran
28 Points
6 years ago
At the instant , where the particle is at height 3R , following things are taken into concern 
The total mechanical energy is conserved , that is
  • The KE required by the particle to reach height 3R , is equal to the GPE ( Gravitational potential energy) at the point 3R from the surface of earth
Therefore , 
The total height = height from surface + radius of earth
= 3R + R = 4R
Then , we have ;
KE = GPE
½mVA2  =  GMm/4R  ( VA = Velocity at 3R from surface )
Solving for VA ,
We get :  VA  = \sqrt{2GM/4R}
                     = \sqrt{GM/2R} (\sqrt{2} / \sqrt{2}) ( Multiply and divide \sqrt{2} )
                      =\sqrt{\frac{2GM}{R}} ( \frac{1}{2})
 
                       =\frac{_{Ve}}{2} ( Ve  = Escape velocity of earth
                       
                       =  \frac{11.2 Km/s}{2} 
                      
                      = 5.6 Km/s

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