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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Physics
Chapter
Motion in Two Dimensions

BITSAT 2021 · Physics · Motion in Two Dimensions

A gun fires two bullets at 60^ ^ and 30^ ^ with horizontal. The...

A gun fires two bullets at 60∘60^{{}^{\circ}} and 30∘30^{{}^{\circ}} with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

Options

  1. A2:12: 1
  2. B3:13: 1
  3. C4:14: 1
  4. D1:11: 1

Correct answer

B. 3:13: 1

Step-by-step solution

The bullets are fired at the same initial speed HH′=\mathrmu2sin⁡260∘2g×2g\mathrmu2sin⁡230∘=sin⁡260∘sin⁡230∘=(3/2)2(1/2)2=31\begin{array}{l} \frac{\mathrm{H}}{\mathrm{H}^{\prime}}=\frac{\mathrmu^{2} \sin ^{2} 60^{{}^{\circ}}}{2 \mathrm{ g}} \times \frac{2 \mathrm{ g}}{\mathrmu^{2} \sin ^{2} 30^{{}^{\circ}}}=\frac{\sin ^{2} 60^{{}^{\circ}}}{\sin ^{2} 30^{{}^{\circ}}} \\ =\frac{(\sqrt{3} / 2)^{2}}{(1 / 2)^{2}}=\frac{3}{1} \end{array}
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