A field surveyor analyzing a topographical map with a scale of 1 : 50,000 measures a strai… — JAMB UTME

A field surveyor analyzing a topographical map with a scale of $1 : 50,000$ measures a straight line distance of $4\text{ cm}$ along a road connecting Hilltop Village at an elevation of $350\text{ m}$ and Valley Junction at an elevation of $150\text{ m}$ . What is the gradient of the road between these two settlements?

$1 \text{ in } 10$ Cevap
B
$1 \text{ in } 1,000$
C
$1 \text{ in } 8$
D
$1 \text{ in } 1$

Cevap

The gradient of the road is

1 \text{ in } 10

The gradient is determined by dividing Vertical Interval (VI) by Horizontal Equivalent (HE). With a VI of

200\text{ m}

(

350\text{ m} - 150\text{ m}

) and a ground distance HE of

2,000\text{ m}

(

4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}

), the ratio

\frac{200}{2,000}

simplifies to

\frac{1}{10}

1 \text{ in } 10

Adım Adım Çözüm

Calculate the Vertical Interval (VI)

\text{VI} = 350\text{ m} - 150\text{ m} = 200\text{ m}

Vertical Interval is the difference in elevation between the two points.

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}

Horizontal Equivalent is the actual ground distance converted to the same unit as VI.

Compute the slope gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{2,000\text{ m}} = \frac{1}{10}

1 \text{ in } 10

Gradient is defined as the ratio of Vertical Interval to Horizontal Equivalent.

Anahtar Kavram

Topographic Slope and Gradient Calculation

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