On a topographical map, the vertical difference between two points, X and Y, is 100\text{ … — JAMB UTME

On a topographical map, the vertical difference between two points, X and Y, is $100\text{ m}$ . If the horizontal distance separating them on the ground is $2\text{ km}$ , what is the gradient of the slope between Point X and Point Y?

1 in 20Cevap
B
1 in 2
C
1 in 200
D
20 to 1

Cevap

The gradient between Point X and Point Y is 1 in 20.

The vertical interval is

100\text{ m}

and the horizontal equivalent is

2\text{ km}

. Converting

2\text{ km}

into metres gives

2,000\text{ m}

. Applying the slope gradient formula

\frac{\text{VI}}{\text{HE}} = \frac{100\text{ m}}{2,000\text{ m}} = \frac{1}{20}

gives a gradient of

1\text{ in } 20

Adım Adım Çözüm

Identify the Vertical Interval (VI) and Horizontal Equivalent (HE)

\text{VI} = 100\text{ m}

and

\text{HE} = 2\text{ km}

Gradient calculation requires both vertical elevation change and horizontal ground distance.

Convert Horizontal Equivalent into metres so both measurements share identical units

\text{HE} = 2\text{ km} \times 1,000 = 2,000\text{ m}

Gradient is a unitless ratio, requiring numerator and denominator to be in the same unit.

Calculate gradient using the formula

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

\text{Gradient} = \frac{100\text{ m}}{2,000\text{ m}} = \frac{1}{20}

Simplifying the fraction yields a ratio of

1\text{ in } 20

Anahtar Kavram

Slope Gradient Calculation on Topographical Maps

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Adım Adım Çözüm

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