A topographic map drawn at a scale of 1 : 25,000 shows a hillside where point P on a ridge… — JAMB UTME

A topographic map drawn at a scale of $1 : 25,000$ shows a hillside where point P on a ridge has an elevation of $580\text{ m}$ and point Q near a river valley has an elevation of $430\text{ m}$ . If the straight-line distance between P and Q measured on the map is $7.2\text{ cm}$ , what is the value of $x$ when the average gradient between the two points is expressed in the ratio form $1 : x$ ?

Cevap: 12

Cevap

The numerical value of

x

in the gradient ratio

1 : x

is 12.

To find the gradient ratio

1 : x

, first calculate the Vertical Interval (VI) by subtracting

430\text{ m}

from

580\text{ m}

, which gives

150\text{ m}

. Next, calculate the Horizontal Equivalent (HE) by multiplying the

7.2\text{ cm}

map distance by the scale factor of

25,000

, giving

180,000\text{ cm}

1,800\text{ m}

. Finally, divide VI by HE:

\frac{150\text{ m}}{1,800\text{ m}} = \frac{1}{12}

. Expressed in the form

1 : x

x = 12

Adım Adım Çözüm

Calculate the Vertical Interval (VI)

VI = 150 m

Subtract the lower elevation (430 m) from the higher elevation (580 m) to determine the vertical height difference.

Calculate the Horizontal Equivalent (HE) in meters

HE = 1,800 m

Multiply the map measurement of 7.2 cm by 25,000 to obtain ground distance in cm (180,000 cm), then divide by 100 to convert to meters.

Compute the gradient ratio and solve for x

Gradient = 1 / 12, giving x = 12

Divide the Vertical Interval by the Horizontal Equivalent: 150 m / 1,800 m = 1 / 12.

Anahtar Kavram

Slope and Gradient Calculation from Topographic Maps

Tahmini Süre:1m 30s

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