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JEE Main 7-April-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 7-April-2025 Paper - Shift 14 Marks
MCQ
Two projectiles are fired from ground with same initial speeds from same point at angles $\left(45^{\circ}+\alpha\right)$ and $\left(45^{\circ}-\alpha\right)$ with horizontal direction. The ratio of their times of flights is
  • A
    1
  • B
    $\frac{1-\tan \alpha}{1+\tan \alpha}$
  • C
    $\frac{1+\sin 2 \alpha}{1-\sin 2 \alpha}$
  • D
    $\frac{1+\tan \alpha}{1-\tan \alpha}$
✓

Answer

D. $\frac{1+\tan \alpha}{1-\tan \alpha}$
$\theta_{1}=45+\alpha ; \theta_{2}=45-\alpha$
Time of flight, $\mathrm{T}=\frac{2 \mathrm{v} \sin \theta}{\mathrm{g}}$
$\frac{T_{1}}{T_{2}}=\frac{\sin (45+\alpha)}{\sin (45-\alpha)}$
$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\frac{1}{\sqrt{2}} \cos \alpha+\frac{1}{\sqrt{2}} \sin \alpha}{\frac{1}{\sqrt{2}} \cos \alpha-\frac{1}{\sqrt{2}} \sin \alpha}$
$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\cos \alpha+\sin \alpha}{\cos \alpha-\sin \alpha}=\frac{1+\tan \alpha}{1-\tan \alpha}$

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