Let $R_{1}$ and $R_{2}$ respectively be the maximum ranges up and down on an inclined plane and $R$

Question

Let $R_{1}$ and $R_{2}$ respectively be the maximum ranges up and down on an inclined plane and $R$ be the maximum range on the horizontal plane. Then, $R_{1}, R, R_{2}$ are in\

Professor PC Thomas Classes · Answer

(c) : Let $	heta$ be the angle of inclined plane with horizontal and $u$ be the velocity of projection of the projectile.\ $	herefore \quad R_{1}=\frac{u^{2}}{g(1+\sin 	heta)}$,\ $R_{2}=\frac{u^{2}}{g(1-\sin 	heta)}, R=\frac{u^{2}}{g}$\ $	herefore \quad \frac{1}{R_{1}}+\frac{1}{R_{2}}=\frac{2 g}{u^{2}}=\frac{2}{R}$\ $\Rightarrow \quad R_{1}, R, R_{2} \in$ H.P.\