On a topographical map drawn to a scale of 1:20,000, a foot trail ascends continuously fro… — JAMB UTME

On a topographical map drawn to a scale of $1:20,000$ , a foot trail ascends continuously from Point A at a contour elevation of $150\text{ m}$ to Point B at a contour elevation of $300\text{ m}$ . If the straight-line map distance between Point A and Point B measures $15.0\text{ cm}$ , what is the average gradient of the slope from Point A to Point B?

A
$1 : 10$
$1 : 20$ Answer
C
$1 : 200$
D
$1 : 500$

Answer

The average gradient of the slope from Point A to Point B is

1 : 20

To determine topographic gradient, calculate the Vertical Interval (

\text{VI}

) as

300\text{ m} - 150\text{ m} = 150\text{ m}

. Convert the map distance (

15.0\text{ cm}

) to ground distance using the map scale (

1:20,000

15.0\text{ cm} \times 20,000 = 300,000\text{ cm} = 3,000\text{ m}

. The ratio

\frac{\text{VI}}{\text{HE}} = \frac{150\text{ m}}{3,000\text{ m}} = \frac{1}{20}

, giving an average gradient of

1 : 20

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 300\text{ m} - 150\text{ m} = 150\text{ m}

The vertical interval represents the total vertical height gained between the starting contour line and the destination contour line.

Convert map distance to ground distance to determine the Horizontal Equivalent (HE)

\text{HE} = 15.0\text{ cm} \times 20,000 = 300,000\text{ cm} = 3,000\text{ m}

Using the map scale ratio of

1:20,000

, every

1\text{ cm}

on the map corresponds to

20,000\text{ cm}

(

200\text{ m}

) on the actual terrain.

Compute the slope gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{150\text{ m}}{3,000\text{ m}} = \frac{1}{20} = 1 : 20

Gradient expresses the ratio of vertical rise to horizontal distance when both measurements are expressed in identical units.

Key Concept

Topographic Slope Gradient Calculation

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