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A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.?
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A street highway leads to foot of the tower. A man standing on the top...
Understanding the Problem
To determine the time taken by the car to reach the foot of the tower, we need to analyze the angles of depression and the distance the car travels.
Given Information
- Initial angle of depression (A) = 30°
- Angle of depression after 6 seconds (B) = 60°
- Time interval = 6 seconds
Drawing the Diagram
Visualize a right triangle formed by the tower height (h), the distance of the car from the tower at the initial angle (d1), and the distance at the second angle (d2).
Calculating Distances
Using the tangent function:
- For angle A (30°):
- tan(30°) = h/d1 => d1 = h/tan(30°) = h/√3
- For angle B (60°):
- tan(60°) = h/d2 => d2 = h/tan(60°) = h/√3
Distance Covered by the Car
The distance covered by the car in 6 seconds is the difference between d1 and d2:
- Distance covered = d1 - d2 = (h/√3) - (h/√3) = h(1 - √3)
Time Calculation
Let the speed of the car be v. The distance covered in 6 seconds can also be expressed as:
- Distance = Speed × Time = v × 6 seconds
Setting the distances equal to each other gives us:
- v × 6 = h(1 - √3)
Now, to find the remaining distance (d2) until the car reaches the tower:
- d2 = h/√3
Using the car's speed to find time (t):
- t = d2/v
Substituting v using the previous equation provides the time taken to reach the tower after 6 seconds.
Final Calculation
Calculate the final time taken by the car to reach the foot of the tower from the second position and conclude the problem.
This approach provides a systematic way to assess the problem using basic trigonometry and distance-speed-time relationships.
To determine the time taken by the car to reach the foot of the tower, we need to analyze the angles of depression and the distance the car travels.
Given Information
- Initial angle of depression (A) = 30°
- Angle of depression after 6 seconds (B) = 60°
- Time interval = 6 seconds
Drawing the Diagram
Visualize a right triangle formed by the tower height (h), the distance of the car from the tower at the initial angle (d1), and the distance at the second angle (d2).
Calculating Distances
Using the tangent function:
- For angle A (30°):
- tan(30°) = h/d1 => d1 = h/tan(30°) = h/√3
- For angle B (60°):
- tan(60°) = h/d2 => d2 = h/tan(60°) = h/√3
Distance Covered by the Car
The distance covered by the car in 6 seconds is the difference between d1 and d2:
- Distance covered = d1 - d2 = (h/√3) - (h/√3) = h(1 - √3)
Time Calculation
Let the speed of the car be v. The distance covered in 6 seconds can also be expressed as:
- Distance = Speed × Time = v × 6 seconds
Setting the distances equal to each other gives us:
- v × 6 = h(1 - √3)
Now, to find the remaining distance (d2) until the car reaches the tower:
- d2 = h/√3
Using the car's speed to find time (t):
- t = d2/v
Substituting v using the previous equation provides the time taken to reach the tower after 6 seconds.
Final Calculation
Calculate the final time taken by the car to reach the foot of the tower from the second position and conclude the problem.
This approach provides a systematic way to assess the problem using basic trigonometry and distance-speed-time relationships.
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A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.?
Question Description
A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.?.
A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.?.
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A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.?, a detailed solution for A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? has been provided alongside types of A street highway leads to foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30° , which is approaching the foot of the tower with an uniform speed. Six seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.? theory, EduRev gives you an
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