A particle is projected with a speed u at an angle θ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called the radius of curvature of the curve at the point.


The approximation for this question will be to take gravity as a central force.


The tangential velocity in this approximated circular motion will be,



Now the central force will be,






This is the radius of the path.


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