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Consider the following map having contours. The scale of map is 1:20,000 as written on the map. The map has shrunk such that 10cm line originally is now 9cm long. The alignment of a road at ruling gradient of 5% is to be fixed from the point P and beyond. What should be the radius of arc (in cm) with P as the centre to get the point of alignment of the next contour on the map? _________ cm
(Important - Enter the numerical value only in the answer)
Correct answer is '1.8'. Can you explain this answer?
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Consider the following map havingcontours. The scale of map is1:20,000...
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Consider the following map havingcontours. The scale of map is1:20,000...
Problem: The map has shrunk from a scale of 1:20,000 to a scale where a 10cm line on the original map is now 9cm long. The task is to fix the alignment of a road with a ruling gradient of 5% from a point P and beyond. We need to find the radius of an arc, with P as the center, that will intersect with the next contour on the map.
Solution:
To solve this problem, we can use the concept of similar triangles and the relationship between radius, arc length, and angle.
Step 1: Determine the actual length of the 10cm line on the original map.
Since the map has shrunk, the actual length of the line can be found by multiplying the length on the current map by the scale factor.
Actual length = 9cm * (1/20,000) = 0.00045 meters
Step 2: Find the vertical distance between the two contours.
The ruling gradient is given as 5%, which means for every 100 meters traveled horizontally, the road rises by 5 meters vertically.
Therefore, the vertical distance between the two contours can be found by multiplying the actual length of the 10cm line by the ruling gradient.
Vertical distance = 0.00045 meters * 5% = 0.0000225 meters
Step 3: Convert the vertical distance to centimeters.
Since the answer is expected in centimeters, we need to convert the vertical distance from meters to centimeters.
Vertical distance = 0.0000225 meters * 100 = 0.00225 centimeters
Step 4: Determine the angle at the center of the arc.
The angle can be found using the relationship between arc length, radius, and angle.
Arc length = 10 centimeters (from the original map)
Radius = unknown (to be determined)
Using the formula: Arc length = radius * angle (in radians), we can rearrange the formula to solve for the angle.
Angle (in radians) = Arc length / radius
Angle (in radians) = 10 centimeters / radius
Step 5: Find the radius of the arc.
To find the radius, we need to convert the angle from radians to degrees.
Using the formula: Angle (in degrees) = Angle (in radians) * (180 / π), we can rearrange the formula to solve for the radius.
Radius = Arc length / (Angle (in degrees) * (π / 180))
Radius = 10 centimeters / (Angle (in degrees) * (π / 180))
Step 6: Substitute the known values and solve for the radius.
Angle (in degrees) = 10 centimeters / (10 / (π / 180))
Angle (in degrees) = 10 centimeters * (π / 180)
Angle (in degrees) ≈ 0.17453 radians
Radius = 10 centimeters / (0.17453 radians * (π / 180))
Radius ≈ 10 centimeters / (0.17453 * 57.2958)
Radius ≈ 10 centimeters / 10.02
Radius ≈ 0.998 centimeters ≈ 1.0 cent
Solution:
To solve this problem, we can use the concept of similar triangles and the relationship between radius, arc length, and angle.
Step 1: Determine the actual length of the 10cm line on the original map.
Since the map has shrunk, the actual length of the line can be found by multiplying the length on the current map by the scale factor.
Actual length = 9cm * (1/20,000) = 0.00045 meters
Step 2: Find the vertical distance between the two contours.
The ruling gradient is given as 5%, which means for every 100 meters traveled horizontally, the road rises by 5 meters vertically.
Therefore, the vertical distance between the two contours can be found by multiplying the actual length of the 10cm line by the ruling gradient.
Vertical distance = 0.00045 meters * 5% = 0.0000225 meters
Step 3: Convert the vertical distance to centimeters.
Since the answer is expected in centimeters, we need to convert the vertical distance from meters to centimeters.
Vertical distance = 0.0000225 meters * 100 = 0.00225 centimeters
Step 4: Determine the angle at the center of the arc.
The angle can be found using the relationship between arc length, radius, and angle.
Arc length = 10 centimeters (from the original map)
Radius = unknown (to be determined)
Using the formula: Arc length = radius * angle (in radians), we can rearrange the formula to solve for the angle.
Angle (in radians) = Arc length / radius
Angle (in radians) = 10 centimeters / radius
Step 5: Find the radius of the arc.
To find the radius, we need to convert the angle from radians to degrees.
Using the formula: Angle (in degrees) = Angle (in radians) * (180 / π), we can rearrange the formula to solve for the radius.
Radius = Arc length / (Angle (in degrees) * (π / 180))
Radius = 10 centimeters / (Angle (in degrees) * (π / 180))
Step 6: Substitute the known values and solve for the radius.
Angle (in degrees) = 10 centimeters / (10 / (π / 180))
Angle (in degrees) = 10 centimeters * (π / 180)
Angle (in degrees) ≈ 0.17453 radians
Radius = 10 centimeters / (0.17453 radians * (π / 180))
Radius ≈ 10 centimeters / (0.17453 * 57.2958)
Radius ≈ 10 centimeters / 10.02
Radius ≈ 0.998 centimeters ≈ 1.0 cent
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Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer?
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Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer?.
Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following map havingcontours. The scale of map is1:20,000 as written on the map. Themap has shrunk such that 10cm lineoriginally is now 9cm long. Thealignment of a road at rulinggradient of 5% is to be fixed fromthe point P and beyond. Whatshould be the radius of arc (in cm)with P as the centre to get the pointof alignment of the next contour onthe map? _________ cm(Important - Enter the numerical value only in the answer)Correct answer is '1.8'. Can you explain this answer?.
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