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A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from 45° to 60°. After this the time required by the vehiele.to reach the bottom of the hill is

A) 12 min 20 sec
B) 13 min
C) 13 min 40 sec
D) 14 mm 24 sec

Correct Answer:



C) 13 min 40 sec

Description for Correct answer:

\( \Large x-\frac{x}{\frac{\sqrt{3}}{\frac{x}{\sqrt{3}}}} \)

\( \Large \frac{\sqrt{3}x-x}{\sqrt{3}}=10 min \)

\( \Large 1\ \ \frac{10}{\frac{\sqrt{3}x-x}{3}} \times x \)

\( \Large x\rightarrow \frac{10\sqrt{3}x}{x(\sqrt{3}-1)}=\frac{10\sqrt{3}}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} \)

\( \Large =\frac{10(3+\sqrt{3})}{2}=5(3+1.732) \)

\( \Large =13.66 \cong 13\ min\ 40\ sec \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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Similar Questions

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