Two projectiles are fired with same initial speed from same point on ground at angles of \(\left(45^\circ -\alpha \right…
Two projectiles are fired with same initial speed from same point on ground at angles of \(\left(45^\circ -\alpha \right)\) and \(\left(45^\circ +\alpha \right)\), respectively, with the horizontal direction. The ratio of their maximum heights attained is :
[JEE Main 2025, 29 Jan (Shift 1)]
\(\frac{1-\sin 2\alpha }{1+\sin 2\alpha }\)
\(\frac{{\left({H}_{\max }\right)}_{1}}{{\left({H}_{\max }\right)}_{2}}=\frac{{u}^{2}{\sin }^{2}(45-\alpha )}{{u}^{2}{\sin }^{2}(45+\alpha )}\\ =\frac{{\left(\frac{1}{\sqrt{2}}\cos \alpha -\frac{1}{\sqrt{2}}\sin \alpha \right)}^{2}}{{\left(\frac{1}{\sqrt{2}}\cos \alpha +\frac{1}{\sqrt{2}}\sin \alpha \right)}^{2}}\\ =\frac{1-\sin 2\alpha }{1+\sin 2\alpha }\)
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