Q) 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 30∘, which is approaching to the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60∘. Find the further time taken by the car to reach the foot of the tower.
Step 1: Diagram for this question:
Here, let’s consider AB is the tower and the car initially at point C and then after 6 seconds, it is at point D.
Given that the angle of depression from point B at Tower top to car at Point C is 300, hence the angle of elevation from C to point B will be 300.
Similarly, since the angle of depression from point B at Tower top to car at Point D is 600, hence the angle of elevation from D to point B will be 600.
Let’s consider distance covered by car from point D to point C is D1 and distance from C to point A at foot of the tower is D2.
Step 2:Find the distance D1:
In Δ ABD,
Similarly, in Δ ABC,
We can see that CD = AD – CD or D1 = AD – D2
Substituting the values from equations (i) and (ii), we get
Step 3: Find the speed of car
Now, it is given that this distance is covered in 6 secs
We know that:
Step 4: Find the time taken to cover CA
Now the car will cover distance with the speed of
We know that:
Substituting the values of distance and speed, we get
Therefore, the distance from point C to point A will be covered in 3 secs.
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