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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Motion in Two Dimensions

NEET 2012 · Physics · Motion in Two Dimensions

The horizontal range and the maximum height of a projectile are...

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

Options

  1. Aθ=tan⁡−1(14)\theta=\tan ^{-1}\left(\frac{1}{4}\right)
  2. Bθ=tan⁡−1(4)\theta=\tan ^{-1}(4)
  3. Cθ=tan⁡−1(2)\theta=\tan ^{-1}(2)
  4. Dθ=45∘\theta=45^{\circ}

Correct answer

B. θ=tan⁡−1(4)\theta=\tan ^{-1}(4)

Step-by-step solution

Given, R=HR=H Range R=u2(2sin⁡θcos⁡θ)gR=\frac{u^2(2 \sin \theta \cos \theta)}{g} Height H=u2sin⁡2θ2gH=\frac{u^2 \sin ^2 \theta}{2 g} Hence, u2(2sin⁡θcos⁡θ)g=u2sin⁡2a2g\frac{u^2(2 \sin \theta \cos \theta)}{g}=\frac{u^2 \sin ^2 a}{2 g}2cos⁡θ=sin⁡θ2tan⁡θ=4θ=tan⁡−1(4)\begin{aligned} 2 \cos \theta & =\frac{\sin \theta}{2} \\ \tan \theta & =4 \\ \theta & =\tan ^{-1}(4) \end{aligned}$$
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