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 $30°to45°$ ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is:

• A. $\frac{9}{2}(\sqrt{3}-1)$
• B. $18(1+\sqrt{3})$
• C. $18(\sqrt{3}-1)$
• D. $9(1+\sqrt{3})$

Answer 1

The correct option is D $9(1+\sqrt{3})$

From the above figure
Let height of tower$=h$
$\Rightarrow A{C}^{\prime }=AB=h\text{and}AC=AB\cot {30}^{\circ }=\sqrt{3}hC{C}^{\prime }=(\sqrt{3}-1)h$
Time taken by the car to reach from $C$ to $C^{\prime }$=18 min
$\Rightarrow$ time taken by the car to reach the foot of the tower $=\frac{18}{\sqrt{3}-1}$ min. =$9(1+\sqrt{3})$ min