🛠️ JEE🧲 Physics

Two projectiles are fired with same initial speed from same point on ground at angles of \(\left(45^\circ -\alpha \right…

Q1 FREE PREVIEW

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)]

a

\(\frac{1-\tan \alpha }{1+\tan \alpha }\)

b

\(\frac{1-\sin 2\alpha }{1+\sin 2\alpha }\)

c

\(\frac{1+\sin \alpha }{1-\sin \alpha }\)

d

\(\frac{1+\sin 2\alpha }{1-\sin 2\alpha }\)

✓ Correct answer: b)

\(\frac{1-\sin 2\alpha }{1+\sin 2\alpha }\)

Explanation

\(\frac{{\left({H}_{\max }\right)}_{1}}{{\left({H}_{\max }\right)}_{2}}=\frac{{u}^{2}{\sin }^{2}(45-\alpha )}{{u}^{2}{\sin }^{2}(45+\alpha )}\\ =\frac{{\left(\frac{1}{\sqrt{2}}\cos \alpha -\frac{1}{\sqrt{2}}\sin \alpha \right)}^{2}}{{\left(\frac{1}{\sqrt{2}}\cos \alpha +\frac{1}{\sqrt{2}}\sin \alpha \right)}^{2}}\\ =\frac{1-\sin 2\alpha }{1+\sin 2\alpha }\)

Practice more JEE Physics PYQs

See every question on Motion in a Plane, or browse the full JEE question bank.

See all questions on Motion in a Plane →