From the top of a 150 m high cliff, an observer notices a car moving away from the base of the cliff. The angle of depression of the car changes from 45° to 30° in 15 seconds. What is the approximate speed of the car?
Show answer & explanation
Correct answer: B
Explanation
Height of the cliff = 150 meters
Horizontal distance of the car at 45° = 150 cot 45° = 150 meters
Horizontal distance of the car at 30° = 150 cot 30° = 150√3 meters
Distance covered in 15 seconds = 150√3 − 150
= 150(√3 − 1)
≈ 150(1.732 − 1)
≈ 109.8 meters
Speed of the car = 109.8/15 ≈ 7.3 m/s