On a topographical map, a surveyor assesses two observation posts: Post X at an elevation … — JAMB UTME

On a topographical map, a surveyor assesses two observation posts: Post X at an elevation of $750\text{ m}$ and Post Y at an elevation of $900\text{ m}$ , separated by a straight-line distance of $4.0\text{ km}$ . An intervening ridge crest with a summit elevation of $820\text{ m}$ is located exactly $1.5\text{ km}$ along the line of sight from Post X. Assuming a direct line of sight between the two posts, which of the following statements correctly evaluates their intervisibility?

The posts are not intervisible because the elevation of the line of sight at the ridge location is $806.25\text{ m}$ , which is below the ridge summit elevation of $820\text{ m}$ .Answer
B
The posts are intervisible because the higher station at Post Y ( $900\text{ m}$ ) completely clears the intervening ridge elevation ( $820\text{ m}$ ).
C
The posts are intervisible because the mean elevation between the two posts is $825\text{ m}$ , which is greater than the intervening ridge elevation of $820\text{ m}$ .
D
The posts are not intervisible because the gradient from Post X to the ridge ( $1:21.4$ ) is steeper than the gradient from the ridge to Post Y ( $1:31.25$ ), causing a convex ground depression.

Answer

The posts are not intervisible because the line of sight elevation at the position of the intervening ridge is

806.25\text{ m}

, which is lower than the ridge crest of

820\text{ m}

Intervisibility between two points on a contour map requires that no intervening landform rises above the imaginary straight ray connecting them. Calculating the line of sight height at

1.5\text{ km}

gives

750\text{ m} + \left(\frac{1.5}{4.0} \times 150\text{ m}\right) = 806.25\text{ m}

. Because the intervening ridge reaches

820\text{ m}

, it obstructs the view, making the posts non-intervisible.

Step-by-Step Solution

Calculate the total vertical height difference between Post X and Post Y.

Vertical Difference

= 900\text{ m} - 750\text{ m} = 150\text{ m}

Establishes the total elevation gain along the

4.0\text{ km}

line of sight.

Determine the proportional vertical rise along the line of sight at a distance of

1.5\text{ km}

from Post X.

Proportional Rise

= \frac{1.5\text{ km}}{4.0\text{ km}} \times 150\text{ m} = 0.375 \times 150\text{ m} = 56.25\text{ m}

Determines how much elevation the line of sight gains over the distance to the intervening ridge.

Calculate the absolute elevation of the line of sight above sea level at the ridge position.

Line of Sight Elevation

= 750\text{ m} + 56.25\text{ m} = 806.25\text{ m}

Provides the baseline height of the visual ray path at the obstacle's location.

Compare the line of sight elevation with the actual ground elevation of the ridge summit.

Ground Elevation (

820\text{ m}

)

>

Line of Sight Elevation (

806.25\text{ m}

). Intervisibility is obstructed.

If the terrain height is greater than the line of sight height, the view between the two points is blocked.

Key Concept

Intervisibility and Profile Line of Sight Analysis

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