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A straight highway leads to the foot of a tower. A man standin

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A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{o}$ , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{o}$ . Find the time taken by the car to reach the foot of the tower from this point.

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A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of

30^{o}

, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be

60^{o}

. Find the time taken by the car to reach the foot of the tower from this point.

13 mins ago

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Text solutionVerified

Let

D C = x, BC = y, A C = d

tan 30 = \frac{CO}{A C} = \frac{x}{d} = 3

....(1)

tan 60 = 3 = \frac{D C}{BC} = \frac{x}{y}

...(2)

from (1) and (2)

d = 3 x = 3 (3 y) = 3 y

∴ s p ee d = \frac{d i s t an ce}{t im e}

from A to B

speed

= \frac{d - y}{6}

required

time

= \frac{distance (from B to c)}{speed}

= \frac{y}{\frac{d - y}{6}}

= \frac{6 y}{d - y}

(∵ d - 3 y)

= \frac{6 y}{3 y - y}

= \frac{6 y}{2 y}

= 3

sec

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Question Text	A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{o}$ , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{o}$ . Find the time taken by the car to reach the foot of the tower from this point.
Answer Type	Text solution:1
Upvotes	150