1.  A man standing on the terrace of a building watches a car speeding towards him. If at that particular instant the car is 200 m away from the building makes an angle of depression of 60° with the man’s eye and after 8 seconds the angle of depression is 30°, what is the speed of the car?
A. 15 m/s
B. 25 m/s
C. 16.67 m/s
D. Cannot be determined

Answer: Option C

Explanation:

Let AB be the building and the man is standing at A.

When the car is 200m away from the building, the angle of depression is 60°

tan 60° = BD/AB = 3

 200/AB = 3

 AB = 115.47 m

 tan30° =BC/AB = x/115.47 = 1/ 3

 x = 66.67

Now, the car travels distance CD in 8 seconds

CD = BD – BC = 200 – 66.67 = 133.33 m

Speed = 133.33/8 = 16.67 m/s