On a topographical map drawn to a scale of 1 : 40,000, a communications cable line is plan… — JAMB UTME

On a topographical map drawn to a scale of $1 : 40,000$ , a communications cable line is planned between Trigonometrical Station $P$ at an elevation of $680\text{ m}$ and Spot Height $Q$ at an elevation of $200\text{ m}$ . If the straight-line distance measured between $P$ and $Q$ on the map is $12\text{ cm}$ , what is the average gradient of the slope between these two points expressed as a percentage?

$10\%$ Cevap
B
$0.1\%$
C
$14.17\%$
D
$4\%$

Cevap

The average gradient of the slope expressed as a percentage is

10\%

The slope gradient is calculated by dividing the Vertical Interval (

480\text{ m}

) by the Horizontal Equivalent (

4,800\text{ m}

). Multiplying the ratio

\frac{480}{4,800} = 0.10

100

yields

10\%

Adım Adım Çözüm

Calculate the Vertical Interval (VI)

\text{VI} = 680\text{ m} - 200\text{ m} = 480\text{ m}

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

Calculate the Horizontal Equivalent (HE) in meters

\text{Ground distance} = 12\text{ cm} \times 40,000 = 480,000\text{ cm} = 4,800\text{ m}

Multiply the map distance by the scale factor and convert from centimeters to meters (

100\text{ cm} = 1\text{ m}

Compute the slope gradient as a percentage

\text{Gradient (\%)} = \left( \frac{\text{VI}}{\text{HE}} \right) \times 100 = \left( \frac{480\text{ m}}{4,800\text{ m}} \right) \times 100 = 10\%

Gradient percentage is defined as the ratio of Vertical Interval to Horizontal Equivalent multiplied by 100.

Anahtar Kavram

Slope and Gradient Calculation on Topographic Maps

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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