A particle is projected vertically with speed V from the surface of the earth. Maximum height attained by the particle, in terms of the radius of earth R , V and g is ( V escape velocity, g is the acceleration due to gravity on the surface of the earth)

Question

A particle is projected vertically with speed V from the surface of the earth. Maximum height attained by the particle, in terms of the radius of earth R , V and g is ( V escape velocity, g is the acceleration due to gravity on the surface of the earth), 3 R V 2 2 g R - 2 V 2, 2 R V 2 3 g R - V 2, R V 2 2 g R - V 2, R V 2 g R - V 2

MARKS App · Accepted Answer

1 2 m V 2 - G M m R = - G M m R + h 1 2 V 2 - G M R 2 ⋅ R = - G m R 2 R 2 ( R + h ) 1 2 V 2 - g R = - g R 2 ( R + h ) R + h = - 2 g R 2 V 2 - 2 g R h = - 2 g R 2 V 2 - 2 g R - R h = - R V 2 V 2 - 2 g R h = R V 2 2 g R - V 2

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