A particle is projected at $t = 0$ with velocity $u$ at angle $ heta$ with the horizontal. Then the

Question

A particle is projected at $t = 0$ with velocity $u$ at angle $	heta$ with the horizontal. Then the ratio of the tangential acceleration and the radius of curvature at the point of projection is:

Professor PC Thomas Classes · Answer

At projection, tangential acc $a_t = g\sin	heta$, normal acc $a_n = g\cos	heta$. Radius $R = u^2/a_n = u^2/(g\cos	heta)$. Ratio $a_t/R = (g\sin	heta)/(u^2/g\cos	heta) = g^2\sin	heta\cos	heta/u^2 = \frac{g^2\sin 2	heta}{2u^2}$.