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 60°, 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 30°. Find the time taken by the car to reach the foot of the tower from this point.
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Answer:
The time taken by the car to reach the foot of the tower is 3 sec.
Step-by-step explanation:
Let the height of tower be AD and the starting point of the car be at point Band after 6 sec let the car b at point C. The angles of the depression of the car from the top A of the tower at point B and C are 60° and 30° respectively.
Distance travelled by the car from the starting point towards the tower in 6 sec=BC
Distanced travelled by the car after 6 sec towards the tower=CD
In ΔABD
tan 60°=AD/BD
√3=AD/BD
BD=AD√3-----(1)
InΔACD
tan 30°=AC/CD
1/√3=AD/CD
AD=CD√3-----(2)
From eq (1) and (2)
BD=CD√3 x √3
BC+CD=3 CD
BC=2CD
Speed of the car to cover distance BC in 6 sec=distance / speed
BC/6
= 2CD/6
=CD/3
Speed of the car 3m/s
∴the time taken by the car to reach the foot of the tower from point C is 3 sec.