A topographical map extract drawn to a scale of 1 : 100,000 shows a footbridge over a stre… — JAMB UTME

A topographical map extract drawn to a scale of $1 : 100,000$ shows a footbridge over a stream at an elevation of $250\text{ m}$ and a forest observation tower situated on a hilltop at an elevation contour of $450\text{ m}$ . If the straight-line distance between the bridge and the tower measured on the map is $4\text{ cm}$ , what is the average gradient of the slope between these two locations?

$1\text{ in } 20$ Answer
B
$1\text{ in } 200$
C
$1\text{ in } 2000$
D
$1\text{ in } 8.9$

Answer

The gradient between the two points is

1\text{ in } 20

The gradient of a slope is computed as the Vertical Interval (VI) divided by the Horizontal Equivalent (HE). The vertical interval is

450\text{ m} - 250\text{ m} = 200\text{ m}

. Using the map scale of

1 : 100,000

, a map distance of

4\text{ cm}

equals

400,000\text{ cm}

4,000\text{ m}

on the ground. Dividing

200\text{ m}

4,000\text{ m}

simplifies to

\frac{1}{20}

, expressed as

1\text{ in } 20

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 450\text{ m} - 250\text{ m} = 200\text{ m}

Vertical interval is the difference in elevation between the two points.

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 4\text{ cm} \times 100,000 = 400,000\text{ cm} = 4,000\text{ m}

Multiply map distance by the scale factor to get real-world distance, then convert centimeters to meters.

Calculate the slope gradient

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{4,000\text{ m}} = \frac{1}{20}

Gradient is expressed as the ratio of Vertical Interval to Horizontal Equivalent in identical measurement units.

Key Concept

Slope gradient determination using Vertical Interval (VI) and Horizontal Equivalent (HE)

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic