Examkin

Soru

Zorluk: OrtaContour Lines and Relief Representation

On a topographical map with a scale of 1:50,0001 : 50,000, two hilltops are located at elevations of 750 m750\text{ m} and 450 m450\text{ m} respectively. If the straight-line distance separating the two hilltops on the map is 6 cm6\text{ cm}, what is the average gradient between them?

  1. 1 in 101\text{ in }10Cevap
  2. B
    1 in 501\text{ in }50
  3. C
    1 in 1001\text{ in }100
  4. D
    1 in 41\text{ in }4

Cevap

The average gradient between the two hilltops is 1 in 101\text{ in }10.
The vertical interval (VI) is the difference in elevation: 750 m−450 m=300 m750\text{ m} - 450\text{ m} = 300\text{ m}. The horizontal equivalent (HE) is the ground distance: 6 cm×50,000=300,000 cm=3,000 m6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}. The gradient is VIHE=3003,000=110\frac{\text{VI}}{\text{HE}} = \frac{300}{3,000} = \frac{1}{10}, expressed as 1 in 101\text{ in }10.

Adım Adım Çözüm

1
Calculate the Vertical Interval (VI)
VI=750 m−450 m=300 m\text{VI} = 750\text{ m} - 450\text{ m} = 300\text{ m}
Gradient requires the difference in elevation between the two specified points.
2
Calculate the Horizontal Equivalent (HE) on the ground in meters
HE=6 cm×50,000=300,000 cm=3,000 m\text{HE} = 6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}
Map distance must be converted to actual ground distance using the representative fraction scale.
3
Calculate the gradient using the formula Gradient=VIHE\text{Gradient} = \frac{\text{VI}}{\text{HE}}
Gradient=300 m3,000 m=110\text{Gradient} = \frac{300\text{ m}}{3,000\text{ m}} = \frac{1}{10} or 1 in 101\text{ in }10
Dividing the vertical interval by the horizontal equivalent in identical units yields the ratio slope.

Anahtar Kavram

Topographic gradient calculation from map scale and elevation differences
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Contour Lines and Relief Representation

Bu konudan daha fazla soru