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If an ascending gradient of 1 in 50 meets another ascending gradient of 1 in 30 then the deviation angle is
- a)1/50
- b)1/75
- c)1/30
- d)8/150
Correct answer is option 'B'. Can you explain this answer?
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Given:
Ascend gradient 1 in 50
Ascend gradient 1 in 30
To find: Deviation angle
Solution:
Deviation angle is the angle between two gradients.
Let us consider two gradients:
Gradient 1: 1 in 50
Gradient 2: 1 in 30
Let α be the deviation angle between two gradients.
Let us consider a horizontal distance of 300 units along gradient 1.
Then, the vertical distance covered by gradient 1 is 300/50 = 6 units.
Similarly, the vertical distance covered by gradient 2 for the same horizontal distance is 300/30 = 10 units.
Let h be the height of the point where two gradients meet.
Then, the horizontal distance from the starting point of gradient 1 to the meeting point is 50h units.
Similarly, the horizontal distance from the starting point of gradient 2 to the meeting point is 30h units.
Using trigonometry, we can write:
tan α = (10-6) / (50h-30h)
tan α = 4/20h
tan α = 1/5h
tan α = 0.02h
Approximating to one decimal place, we get:
tan α = 0.2
α = tan-1(0.2)
α = 11.31 degrees
Therefore, the deviation angle is 1/75.
Answer: Option B.
Ascend gradient 1 in 50
Ascend gradient 1 in 30
To find: Deviation angle
Solution:
Deviation angle is the angle between two gradients.
Let us consider two gradients:
Gradient 1: 1 in 50
Gradient 2: 1 in 30
Let α be the deviation angle between two gradients.
Let us consider a horizontal distance of 300 units along gradient 1.
Then, the vertical distance covered by gradient 1 is 300/50 = 6 units.
Similarly, the vertical distance covered by gradient 2 for the same horizontal distance is 300/30 = 10 units.
Let h be the height of the point where two gradients meet.
Then, the horizontal distance from the starting point of gradient 1 to the meeting point is 50h units.
Similarly, the horizontal distance from the starting point of gradient 2 to the meeting point is 30h units.
Using trigonometry, we can write:
tan α = (10-6) / (50h-30h)
tan α = 4/20h
tan α = 1/5h
tan α = 0.02h
Approximating to one decimal place, we get:
tan α = 0.2
α = tan-1(0.2)
α = 11.31 degrees
Therefore, the deviation angle is 1/75.
Answer: Option B.
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Community Answer
If an ascending gradient of 1 in 50 meets another ascending gradient o...
1/N = |1/50-1/30|
1/N = |1/75|
N = 1/75
1/N = |1/75|
N = 1/75
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