Match each topographic map slope calculation scenario on the left with its corresponding c… — JAMB UTME

Match each topographic map slope calculation scenario on the left with its corresponding calculated gradient representation on the right.

A vertical rise of $50\text{ m}$ measured across a map distance of $4\text{ cm}$ on a map scale of $1 : 25,000$ $1 \text{ in } 20$ ( $5.0\%$ )
An elevation change from $120\text{ m}$ to $320\text{ m}$ along a road measuring $5\text{ cm}$ on a $1 : 50,000$ topographical map $1 \text{ in } 12.5$ ( $8.0\%$ )
A hill slope rising $150\text{ m}$ across a map line of $6\text{ cm}$ drawn to a scale of $1 : 25,000$ $1 \text{ in } 10$ ( $10.0\%$ )
A terrain transect crossing $4$ contour intervals of $20\text{ m}$ each, spanning a map distance of $4\text{ cm}$ at $1 : 100,000$ scale $1 \text{ in } 50$ ( $2.0\%$ )

Answer

The correct pairings are: (1) A vertical rise of 50 m across 4 cm on a 1:25,000 map matches 1 in 20 (5.0%); (2) An elevation change from 120 m to 320 m over 5 cm on a 1:50,000 map matches 1 in 12.5 (8.0%); (3) A rise of 150 m over 6 cm on a 1:25,000 map matches 1 in 10 (10.0%); (4) Crossing 4 contour intervals of 20 m across 4 cm at 1:100,000 scale matches 1 in 50 (2.0%).

Each scenario is accurately paired by converting the map distance to actual ground distance in meters using the given scale, determining the vertical interval, and computing the gradient as a ratio (1 in N) and percentage.

Step-by-Step Solution

Convert the map distance for each scenario into the ground horizontal distance (Horizontal Equivalent, HE) in meters using the designated map scale.

Scenario 1:

4\text{ cm} \times 25,000 / 100 = 1,000\text{ m}

. Scenario 2:

5\text{ cm} \times 50,000 / 100 = 2,500\text{ m}

. Scenario 3:

6\text{ cm} \times 25,000 / 100 = 1,500\text{ m}

. Scenario 4:

4\text{ cm} \times 100,000 / 100 = 4,000\text{ m}

Map scale Representative Fractions convert map measurements to real ground horizontal distances, which must be expressed in meters to match the unit of Vertical Interval.

Calculate the total height difference (Vertical Interval, VI) in meters for each terrain scenario.

Scenario 1:

\text{VI} = 50\text{ m}

. Scenario 2:

\text{VI} = 320\text{ m} - 120\text{ m} = 200\text{ m}

. Scenario 3:

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

. Scenario 4:

\text{VI} = 4 \text{ intervals} \times 20\text{ m} = 80\text{ m}

Vertical Interval represents the net vertical relief difference between the start and end points of the transect.

Compute the gradient ratio (VI / HE) and express it both as a simple ratio (1 in N) and as a percentage slope.

Scenario 1:

\frac{50}{1,000} = \frac{1}{20} \rightarrow 1 \text{ in } 20

(

5.0\%

). Scenario 2:

\frac{200}{2,500} = \frac{1}{12.5} \rightarrow 1 \text{ in } 12.5

(

8.0\%

). Scenario 3:

\frac{150}{1,500} = \frac{1}{10} \rightarrow 1 \text{ in } 10

(

10.0\%

). Scenario 4:

\frac{80}{4,000} = \frac{1}{50} \rightarrow 1 \text{ in } 50

(

2.0\%

Gradient formula is

\text{Gradient} = \frac{\text{Vertical Interval (VI)}}{\text{Horizontal Equivalent (HE)}}

Key Concept

Slope and Gradient Calculation from Topographical Maps

Estimated Time:3m 0s

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