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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=h
In APB,tan30=ABPB
13=hx+h
x+h=h3
x=h(31)
Thus,speed=h(31)12 m/min
Time for remaining distance,
hh(31)12=12(3+1)31
=122(3+1)
=6(3+1)
Time=6(3+1) minutes

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