Question

A stone is projected with speed $u$ and angle of projection is $\theta$. Find radius of curvature at $t=0$.

• A. $\frac{u^{2}co{s}^2\theta }{g}$
• B. $\frac{u^2}{gsin\theta }$
• C. $\frac{u^2}{gcos\theta }$
• D. $\frac{u^{2}si{n}^2\theta }{g}$

Answer 1

The correct option is C $\frac{u^2}{gcos\theta }$

Let the radius of curvature at $t=0$ be $r$.

The intitial velocity is $u$ at angle $\theta$ with horizontal. The centripital accceleration (perpendicular to the initial velocity) is $gcos\theta =\frac{u^2}{r}$. So the radius of curvature is $\frac{u^2}{gcos\theta }$