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Standard XII

Mathematics

Geometric Interpretation of Def.Int as Limit of Sum

A gun fires t...

Question

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

2 : 1

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3 : 1

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4 : 1

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1 : 1

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Solution

The correct option is A $3 : 1$
The bullets are fired at the same initial speed. Hence
$\frac{h}{h^{'}} = \frac{u^{2} {sin}^{2} 60^{\circ}}{2 g} \times \frac{2 g}{u^{2} {sin}^{2} 30^{\circ}}$

$= \frac{{sin}^{2} 60^{\circ}}{{sin}^{2} 30^{\circ}} = \frac{3}{1}$ .

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

The correct option is A 3:1The bullets are fired at the same initial speed. Hencehh′=u2sin260∘2g×2gu2sin230∘=sin260∘sin230∘=31.

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

The correct option is A $3 : 1$
The bullets are fired at the same initial speed. Hence
$\frac{h}{h^{'}} = \frac{u^{2} {sin}^{2} 60^{\circ}}{2 g} \times \frac{2 g}{u^{2} {sin}^{2} 30^{\circ}}$

$= \frac{{sin}^{2} 60^{\circ}}{{sin}^{2} 30^{\circ}} = \frac{3}{1}$ .