Match each topographic relief profile scenario to its corresponding calculated slope gradi… — JAMB UTME

Match each topographic relief profile scenario to its corresponding calculated slope gradient expressed both as a ratio ( $1 \text{ in } N$ ) and as a percentage gradient.

Trigonometric beacon at $450\text{ m}$ to river confluence at $150\text{ m}$ ; map distance is $6\text{ cm}$ on a scale of $1:50,000$ . $1 \text{ in } 10$ ( $10\%$ )
Valley floor at elevation $180\text{ m}$ rising to a plateau rim at $420\text{ m}$ ; map distance is $2.4\text{ cm}$ on a scale of $1:25,000$ . $1 \text{ in } 2.5$ ( $40\%$ )
Proposed railway track passing from elevation $100\text{ m}$ to $220\text{ m}$ ; map distance is $12\text{ cm}$ on a scale of $1:50,000$ . $1 \text{ in } 50$ ( $2\%$ )
Scarp face intersecting $5$ consecutive contour lines of interval $25\text{ m}$ ; map distance across the scarp is $0.8\text{ cm}$ on a scale of $1:50,000$ . $1 \text{ in } 4$ ( $25\%$ )

Answer

Trigonometric beacon to river confluence matches

1 \text{ in } 10

(

10\%

); Valley floor to plateau rim matches

1 \text{ in } 2.5

(

40\%

); Proposed railway track matches

1 \text{ in } 50

(

2\%

); Scarp face across 5 contour lines matches

1 \text{ in } 4

(

25\%

Each topographic scenario correctly pairs with its calculated gradient ratio and percentage by computing the exact Vertical Interval (difference in height) and Horizontal Equivalent (ground distance derived from map scale).

Step-by-Step Solution

Calculate the Vertical Interval (VI) for each scenario

Scenario 1:

450 - 150 = 300\text{ m}

. Scenario 2:

420 - 180 = 240\text{ m}

. Scenario 3:

220 - 100 = 120\text{ m}

. Scenario 4:

(5-1) \times 25 = 100\text{ m}

VI represents the difference in height between two points.

Calculate the Horizontal Equivalent (HE) in meters for each scenario

Scenario 1:

6\text{ cm} \times 500\text{ m/cm} = 3,000\text{ m}

. Scenario 2:

2.4\text{ cm} \times 250\text{ m/cm} = 600\text{ m}

. Scenario 3:

12\text{ cm} \times 500\text{ m/cm} = 6,000\text{ m}

. Scenario 4:

0.8\text{ cm} \times 500\text{ m/cm} = 400\text{ m}

Convert map distance to ground distance using the representative fraction scale.

Compute the slope gradient ratio (VI / HE) and express as 1 in N and percentage

Scenario 1:

300 / 3000 = 1/10 = 1 \text{ in } 10

(

10\%

). Scenario 2:

240 / 600 = 1/2.5 = 1 \text{ in } 2.5

(

40\%

). Scenario 3:

120 / 6000 = 1/50 = 1 \text{ in } 50

(

2\%

). Scenario 4:

100 / 400 = 1/4 = 1 \text{ in } 4

(

25\%

Gradient is calculated as VI / HE, yielding both ratio 1 in N and percentage slope (VI/HE * 100%).

Key Concept

Slope and Gradient Calculation

Question

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