Q124 / 160 · TS EAMCET 2024 (09 May Shift 1) · Physics

A body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is

  • A
    $1: 4$
  • Correct answer
    B
    $1: 6$
  • C
    $2: 3$
  • D
    $1: 1$

Solution

Horizontal range, $\mathrm{R}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{~g}}$ Maximum height, $\mathrm{H}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}$ $\frac{\mathrm{H}_{\mathrm{P}}}{\mathrm{H}_{\mathrm{Q}}}=\frac{1}{6}$ or, $\mathrm{H}_{\mathrm{P}}: \mathrm{H}_{\mathrm{Q}}=1: 6$

Hence, the correct answer is option: 'B'.

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