A 1.2 , m tall girl spots a balloon moving wi | vedclass

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Question

(D) Let the height of the girl be $h_1 = 1.2 \, m$ and the height of the balloon be $H = 88.2 \, m$. The effective height of the balloon from the girl

Vedclass · Accepted Answer

$100.92 \, m$

Vedclass · Answer

(D) Let the height of the girl be $h_1 = 1.2 \, m$ and the height of the balloon be $H = 88.2 \, m$. The effective height of the balloon from the girl's eye level is $H' = 88.2 - 1.2 = 87 \, m$.In the first position,let the horizontal distance be $x_1$. Then $	an(60^{\circ}) = \frac{87}{x_1} \implies x_1 = \frac{87}{\sqrt{3}} = 29\sqrt{3} \, m$.In the second position,let the horizontal distance be $x_2$. Then $	an(30^{\circ}) = \frac{87}{x_2} \implies x_2 = 87\sqrt{3} \, m$.The distance travelled by the balloon is $d = x_2 - x_1 = 87\sqrt{3} - 29\sqrt{3} = 58\sqrt{3} \, m$.Using $\sqrt{3} \approx 1.732$,$d = 58 	imes 1.732 = 100.456 \, m$. Given the options,the closest value is $100.46 \, m$ (Note: The provided option $100.92$ is the standard textbook answer for this specific problem variant).

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