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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 horizontal road . If it takes 12 min . for the angle of depression of the car to charge from 30 degree to 45 degree. 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
18(31)
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D
6(3+1)
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Solution

## The correct option is D 6(√3+1)Let AB=h be the height of the tower.∠AQB=45∘Now, in △ABQ,tan45∘=ABBQ⇒1=hBQ⇒BQ=hIn △APB,tan30∘=ABPB⇒1√3=hx+h⇒x+h=h√3⇒x=h(√3−1)Thus,speed=h(√3−1)12 m/minTime for remaining distance,hh(√3−1)12=12(√3+1)3−1=122(√3+1)=6(√3+1)Time=6(√3+1) minutes

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