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 , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be . Find the time taken by the car to reach the foot of the tower from this point.
Step 1: Draw the diagram according to the question.
Let be the tower. is the initial and is the final position of the car respectively.
As man is standing at the top of the tower so, Angles of depression are measured from .
is the distance from the foot of the tower to the car.
Step 2: Find relation between and
Now, comparing Height , we get
(Since LHS are same, so RHS are also same)
Here, distance of is half of
Step 3: Find the required time.
Hence, the time taken is also half.
Since, Time taken by car to travel distance
So, Time taken by car to travel .