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Question

# A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizonatal road. If it takes 18 min. for the angle of depression of the car to change from 30° to 45° ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is:

A
9(1+3)
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B
18(1+3)
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C
92(31)
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D
18(31)
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Solution

## The correct option is A 9(1+√3)From the above figure Let height of tower=h ⇒AC′=AB=h and AC=ABcot30∘=√3hCC′=(√3−1)h Time taken by the car to reach from C to C′=18 min ⇒ time taken by the car to reach the foot of the tower =18√3−1 min. =9(1+√3) min

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