Question

a particle is projected from ground at an angle of theta with horizontal with speed u. the ratio of radius of curvature of its trajectory at point of projection to radius of curvature at maximum height is​

Answer 1

Radius of curvature is the value of radius if we assume the particle is moving in a circle at that point.

At the starting point, let the radius of curvature is R. Then,

From the equation of centripetal acceleration,

u2R=g cos θ⇒R=u2g cos θ
When the particle is at its highest point, its velocity is u cos θ. Therefore, the radius of curvature is,

u cos θ2Rmin=g⇒Rmin=u2cos2 θg