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This paper attempts to find the


 minimum time to attain the escape velocity for a single staged rocket if the path of the rocket is along exponential curves. From this calculation, we determine if an ideal path of a rocket can reach escape velocity in the least time.

In this paper, r (radius of lattitute) has been considered according to the position of the rocket.

Keywords: Euler-Lagrange equation, Escape Velocity, Universal Gravitational Constant,G = 6.673 Nm /kg   is defined as the radius of latitude as per position of the rocket (and not the radius of the earth).

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