Cross-Sections and Intervisibility Alıştırma Soruları — JAMB UTME

Soru 1Soru →

A topographic cross-section is constructed from a map with a horizontal scale of $1 : 50{}000$ . If the vertical scale of the cross-section is set at $1\text{ cm}$ to represent $100\text{ m}$ , what is the vertical exaggeration of the cross-section?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The vertical exaggeration of the cross-section is 5.

To find vertical exaggeration, both scales must be in representative fraction (R.F.) form. A vertical scale of

1\text{ cm}

to

100\text{ m}

equals

1 : 10{}000

. Dividing the horizontal scale denominator (

50{}000

) by the vertical scale denominator (

10{}000

) gives a vertical exaggeration of

5

.

Adım Adım Çözüm

1

Convert the vertical scale to a representative fraction

Vertical Scale = 1 : 10,000

Units must be consistent (centimetres to centimetres) to obtain a non-dimensional ratio.

2

Divide the horizontal scale denominator by the vertical scale denominator

50,000 / 10,000 = 5

Vertical exaggeration measures how many times greater the vertical scale is than the horizontal scale.

Anahtar Kavram

Vertical Exaggeration of Cross-Sections

Soru 2Soru →

A physical geographer constructs a cross-section across a ridge on a topographic map with a scale of $1 : 25{}000$ . On the vertical axis of the profile, $1\text{ cm}$ represents an elevation of $20\text{ metres}$ . What is the vertical exaggeration ( $VE$ ) of this cross-section profile?

Cevabı ve açıklamayı göster

Cevap: 12.5

Cevap

The vertical exaggeration of the cross-section profile is 12.5.

To find vertical exaggeration (

VE

), convert both the vertical and horizontal scales to Representative Fractions (RF). The vertical scale of

1\text{ cm} = 20\text{ m}

converts to

1\text{ cm} : 2{}000\text{ cm}

(

1 : 2{}000

). The horizontal scale is given as

1 : 25{}000

. Dividing the horizontal scale denominator (

25{}000

) by the vertical scale denominator (

2{}000

) yields

12.5

.

Adım Adım Çözüm

1

Convert the vertical scale to a unitless Representative Fraction (RF)

Vertical Scale =

1\text{ cm} : 20\text{ m} = 1\text{ cm} : 2{}000\text{ cm} = 1 : 2{}000

Both horizontal and vertical scales must be expressed in the same unit (centimetres) to enable direct comparison as representative fractions.

2

State the horizontal scale as a Representative Fraction (RF)

Horizontal Scale =

1 : 25{}000

The map scale provides the horizontal ratio between map distance and ground distance.

3

Apply the vertical exaggeration formula

VE = \frac{\text{Vertical Scale (RF)}}{\text{Horizontal Scale (RF)}} = \frac{1 / 2{}000}{1 / 25{}000} = \frac{25{}000}{2{}000}

Vertical exaggeration measures how many times larger the vertical scale is relative to the horizontal scale.

4

Perform the final division

VE = 12.5

Dividing 25,000 by 2,000 yields the unitless exaggeration factor of 12.5.

Anahtar Kavram

Vertical Exaggeration of Topographic Profiles

Soru 3Soru →

Assuming an absence of surface obstructions such as trees or tall structures, two observation stations located respectively at the summit and the base of a hill possessing a convex slope are intervisible.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. Two points located at the summit and the base of a convex slope are not intervisible because the outward bulge of the slope in its upper-middle section obstructs the direct line of sight.

Intervisibility between two points on a map depends on whether the relief between them drops below the straight line of sight. On a convex slope, the upper portion has a gentle gradient (contours far apart) while the lower portion is steep (contours close together). This creates a bulging profile where the central terrain rises into the direct sightline between the summit and the valley floor, preventing mutual visibility.

Adım Adım Çözüm

1

Analyze the characteristic contour arrangement and profile of a convex slope.

On a convex slope, contours are widely spaced near the crest (gentle gradient) and closely spaced near the base (steep gradient).

Understanding the physical shape of the land profile is necessary to evaluate the path of the sightline.

2

Evaluate the line of sight between the highest point (summit) and lowest point (base).

The direct line connecting the summit and base passes below the bulging middle section of the hill profile.

Intervisibility requires that no ground point along the cross-section intersects or rises above the straight line connecting the two stations.

3

Determine intervisibility status.

The stations are not intervisible.

Intervening high ground caused by the convex curvature blocks the sightline.

Anahtar Kavram

Intervisibility on Convex vs. Concave Slopes

Soru 4Soru →

A cross-section is constructed from a topographic map drawn at a horizontal scale of $1 : 50\,000$ . If the vertical scale of the cross-section is set such that $1\text{ cm}$ represents $100\text{ m}$ of elevation, what is the vertical exaggeration of the cross-section?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The vertical exaggeration of the cross-section is 5.

To find the vertical exaggeration, both scales must be in representative fraction format. The horizontal scale is

1 : 50\,000

. The vertical scale (

1\text{ cm}

to

100\text{ m}

) equals

1 : 10\,000

. Dividing the horizontal denominator (

50\,000

) by the vertical denominator (

10\,000

) gives a vertical exaggeration of 5.

Adım Adım Çözüm

1

Convert the vertical scale to representative fraction form

Vertical Scale = 1 : 10,000

Both scales must be expressed as dimensionless ratios (RF) in matching units to determine vertical enlargement.

2

Divide the horizontal scale denominator by the vertical scale denominator

VE = 50,000 / 10,000 = 5

Vertical exaggeration quantifies how many times larger the vertical scale is compared to the horizontal scale.

Anahtar Kavram

Vertical Exaggeration in Topographic Profiles

Cross-Sections and Intervisibility

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