On a topographical map drawn to a scale of 1 : 25,000, Point P is situated at a trigonomet… — JAMB UTME

On a topographical map drawn to a scale of $1 : 25,000$ , Point P is situated at a trigonometric station with an elevation of $520\text{ m}$ , while Point Q lies at a stream confluence at an elevation of $370\text{ m}$ . The measured straight-line distance between Point P and Point Q on the map is $15\text{ cm}$ . What is the slope gradient between Point P and Point Q, expressed as the denominator $N$ in the ratio $1 \text{ in } N$ ?

Answer: 25

Answer

The denominator

N

of the slope gradient ratio (

1 \text{ in } N

) is 25.

The Vertical Interval (VI) between Point P and Point Q is

520\text{ m} - 370\text{ m} = 150\text{ m}

. Using the map scale of

1 : 25,000

, the Horizontal Equivalent (HE) is

15\text{ cm} \times 25,000 = 375,000\text{ cm} = 3,750\text{ m}

. Dividing the VI by the HE gives

\frac{150}{3,750} = \frac{1}{25}

. Therefore, the gradient expressed as a ratio is

1 \text{ in } 25

, and the denominator

N

is 25.

Step-by-Step Solution

Determine the Vertical Interval (VI)

\text{VI} = 520\text{ m} - 370\text{ m} = 150\text{ m}

Vertical Interval is the difference in elevation between the higher and lower points.

Calculate the Horizontal Equivalent (HE) in ground units (meters)

\text{HE} = 15\text{ cm} \times 25,000 = 375,000\text{ cm} = 3,750\text{ m}

Horizontal Equivalent is obtained by converting the measured map distance to actual ground distance using the representative fraction scale.

Compute the Gradient Ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{150\text{ m}}{3,750\text{ m}} = \frac{1}{25}

Gradient is the ratio of Vertical Interval to Horizontal Equivalent, both expressed in identical units.

Key Concept

Slope and Gradient Calculation using Representative Fraction Map Scale

Estimated Time:1m 30s

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