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Zorluk: OrtaContour Lines and Relief Representation

On a topographical map with a scale of 1:50,0001 : 50,000, a footpath connects a valley station at an elevation of 250 m250\text{ m} to a mountain peak at 650 m650\text{ m}. If the distance between the two points measured along the footpath on the map is 8 cm8\text{ cm}, what is the average gradient of the slope?

  1. A
    1 in 51\text{ in }5
  2. 1 in 101\text{ in }10Cevap
  3. C
    1 in 201\text{ in }20
  4. D
    1 in 501\text{ in }50

Cevap

The average gradient of the slope between the valley station and the mountain peak is 1 in 101\text{ in }10.
The correct answer is obtained by finding the difference in height between the two points (650 m−250 m=400 m650\text{ m} - 250\text{ m} = 400\text{ m}) and dividing it by the ground horizontal distance (8 cm×500 m/cm=4,000 m8\text{ cm} \times 500\text{ m/cm} = 4,000\text{ m}). The resulting ratio 4004000\frac{400}{4000} simplifies to 1 in 101\text{ in }10.

Adım Adım Çözüm

1
Calculate the Vertical Interval (VI)
VI=650 m−250 m=400 m\text{VI} = 650\text{ m} - 250\text{ m} = 400\text{ m}
Vertical interval is the difference in elevation between the highest and lowest points.
2
Calculate the Horizontal Equivalent (HE) using map scale
HE=8 cm×50,000=400,000 cm=4,000 m\text{HE} = 8\text{ cm} \times 50,000 = 400,000\text{ cm} = 4,000\text{ m}
Map scale of 1:50,0001 : 50,000 means 1 cm1\text{ cm} on map represents 50,000 cm50,000\text{ cm} (500 m500\text{ m}) on the ground.
3
Calculate the gradient ratio
Gradient=VIHE=400 m4,000 m=110\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{400\text{ m}}{4,000\text{ m}} = \frac{1}{10} or 1 in 101\text{ in }10
Gradient is expressed as the ratio of vertical rise to horizontal distance.

Anahtar Kavram

Topographic Gradient Calculation
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Konular

Contour Lines and Relief Representation

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