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Question

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.

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Solution

Particle is projected with speed 'u' at an angle θ. At the highest point the vertical component of velocity is '0'.

So at the point, velocity = u cos θ

centripetal force = mu2 cos2 θr

At highest point

mg=mv2r=mu2 cos2 θr

r=u2 cos2 θg


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