A physical geographer constructs a cross-section across a ridge on a topographic map with … — JAMB UTME

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?

Answer: 12.5

Answer

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

Step-by-Step Solution

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.

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.

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.

Perform the final division

VE = 12.5

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

Key Concept

Vertical Exaggeration of Topographic Profiles

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