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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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A man standing on the terrace of a building watches a car speeding tow...
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/sMost Upvoted Answer
A man standing on the terrace of a building watches a car speeding tow...
Understanding the Problem
The problem involves a man on a terrace observing a car. We need to determine the speed of the car based on angles of depression at two different times.
Given Data
- Initial distance from the car to the building: 200 m
- Initial angle of depression: 60°
- Angle of depression after 8 seconds: 30°
Calculating Heights and Distances
1. Initial Height Calculation:
- Using the angle of depression (60°):
- The height (h) of the terrace can be calculated using the tangent function:
- h = 200 * tan(60°) = 200 * √3
2. Position After 8 Seconds:
- After 8 seconds, the car makes an angle of depression of 30°:
- The new horizontal distance (d) from the building can be calculated:
- h = d * tan(30°)
- d = h / tan(30°) = (200 * √3) / (1/√3) = 600 m
Calculating the Distance Traveled by the Car
- Total Distance Covered:
- Initially, the car was 200 m away and is now 600 m away.
- Distance traveled = 600 m - 200 m = 400 m
Calculating Speed of the Car
- Speed Calculation:
- Speed = Distance / Time
- Speed = 400 m / 8 s = 50 m/s
Conclusion
The calculated speed of the car is incorrect in terms of the options provided. Therefore, if the answer is indeed stated as 16.67 m/s, it suggests a different interpretation or calculation might be needed. The correct approach leads to a clear understanding of the problem's requirements and the progression of the car's movement based on the angles of depression observed.
The problem involves a man on a terrace observing a car. We need to determine the speed of the car based on angles of depression at two different times.
Given Data
- Initial distance from the car to the building: 200 m
- Initial angle of depression: 60°
- Angle of depression after 8 seconds: 30°
Calculating Heights and Distances
1. Initial Height Calculation:
- Using the angle of depression (60°):
- The height (h) of the terrace can be calculated using the tangent function:
- h = 200 * tan(60°) = 200 * √3
2. Position After 8 Seconds:
- After 8 seconds, the car makes an angle of depression of 30°:
- The new horizontal distance (d) from the building can be calculated:
- h = d * tan(30°)
- d = h / tan(30°) = (200 * √3) / (1/√3) = 600 m
Calculating the Distance Traveled by the Car
- Total Distance Covered:
- Initially, the car was 200 m away and is now 600 m away.
- Distance traveled = 600 m - 200 m = 400 m
Calculating Speed of the Car
- Speed Calculation:
- Speed = Distance / Time
- Speed = 400 m / 8 s = 50 m/s
Conclusion
The calculated speed of the car is incorrect in terms of the options provided. Therefore, if the answer is indeed stated as 16.67 m/s, it suggests a different interpretation or calculation might be needed. The correct approach leads to a clear understanding of the problem's requirements and the progression of the car's movement based on the angles of depression observed.
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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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about 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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about 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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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/sb)25 m/sc)16.67 m/sd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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