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 $\displaystyle 30$°, which is approaching the foot of the tower with a uniform speed. Ten seconds later, the angle of depression of the car is found to be $\displaystyle 60$°. Find the time taken by the car to reach the foot of the tower from this point.

\[\begin{aligned} & \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{h}{x+y} \\ & \Rightarrow h=\frac{x+y}{\sqrt{3}} \ldots \ldots . \end{aligned} \] \[\tan 60^{\circ}=\sqrt{3}=\frac{h}{y} \] \[\Rightarrow h=y \sqrt{3} \] Using (i) and (ii), \(\displaystyle \frac{x+y}{\sqrt{3}}=y \sqrt{3}\) \[\Rightarrow y=\frac{x}{2} \] Distance \(\displaystyle x\) is covered in $\displaystyle 10$ sec . ∴ Distance \(\displaystyle y\) is covered in $\displaystyle 5$ sec. ∴ Time taken by car to reach the foot of the tower is 5sec