On a topographical map with a scale of 1:50,000, Point X is situated on a contour line mar… — JAMB UTME

On a topographical map with a scale of $1:50,000$ , Point X is situated on a contour line marked $350\text{ m}$ and Point Y is situated on a contour line marked $500\text{ m}$ . If the measured distance between Point X and Point Y on the map is $6\text{ cm}$ , what is the gradient of the slope between Point X and Point Y?

$1\text{ in } 20$ Answer
B
$1\text{ in } 50$
C
$1\text{ in } 10$
D
$1\text{ in } 2$

Answer

The gradient of the slope between Point X and Point Y is

1\text{ in } 20

(or

1:20

The slope gradient is calculated by dividing the Vertical Interval (difference in elevation:

500\text{ m} - 350\text{ m} = 150\text{ m}

) by the Horizontal Equivalent (actual ground distance:

6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}

). Converting both parameters into meters gives

\frac{150}{3000} = \frac{1}{20}

, which represents a slope ratio of

1\text{ in } 20

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 500\text{ m} - 350\text{ m} = 150\text{ m}

The Vertical Interval is the difference in height between the two contour points.

Calculate the Horizontal Equivalent (HE) in ground measurement

\text{HE} = 6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}

The Representative Fraction scale of

1:50,000

means

1\text{ cm}

on the map represents

50,000\text{ cm}

(

500\text{ m}

) on the ground.

Calculate the slope gradient formula

\text{Gradient} = \frac{\text{VI}}{\text{HE}}

\text{Gradient} = \frac{150\text{ m}}{3,000\text{ m}} = \frac{1}{20}

Dividing the vertical height by the horizontal distance in identical units expresses the slope as a ratio.

Key Concept

Topographic Slope Gradient Calculation

Estimated Time:2m 0s

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