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A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' $\theta$ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, $\theta$, is then given by:
Explanation
Speed of particle to complete one revolution, $(U) = 2\pi R/T$ Particle is projected with same speed (U) at an angle q to the horizontal $\therefore$ Maximum Height $(H) = U^{2}\sin^{2} \theta/2g$ or, $U^{2}\sin^{2} \theta/2g = 4R$ [$\because H = 4R$ given] $\Rightarrow \sin^{2} \theta = 8gR/U^{2}$ or, $\sin^{2} \theta = 8gRT^{2}/4\pi^{2}R^{2} = 2gT^{2}/\pi^{2}R$ (using equation (i)) $\therefore \theta = \sin^{-1}(2gT^{2}/\pi^{2}R)^{1/2}$
