Question

A particle is thrown vertically upwards with velocity 11.2km/s from the surface of the earth calculate its velocity at height 3r

Answer 1

t 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