Match each set of topographic relief measurements to its corresponding slope gradient rati… — JAMB UTME

Match each set of topographic relief measurements to its corresponding slope gradient ratio ( $1 \text{ in } N$ ).

Vertical Interval of $20\text{ m}$ across a Horizontal Distance of $200\text{ m}$ $1 \text{ in } 10$
Vertical Interval of $50\text{ m}$ across a Horizontal Distance of $1,000\text{ m}$ $1 \text{ in } 20$
Vertical Interval of $100\text{ m}$ across a Horizontal Distance of $500\text{ m}$ $1 \text{ in } 5$
Vertical Interval of $10\text{ m}$ across a Horizontal Distance of $500\text{ m}$ $1 \text{ in } 50$

Vertical Interval

20\text{ m}

/ Distance

200\text{ m}

matches

1 \text{ in } 10

; Vertical Interval

50\text{ m}

/ Distance

1,000\text{ m}

matches

1 \text{ in } 20

; Vertical Interval

100\text{ m}

/ Distance

500\text{ m}

matches

1 \text{ in } 5

; Vertical Interval

10\text{ m}

/ Distance

500\text{ m}

matches

1 \text{ in } 50

Each slope measurement set correctly matches its calculated gradient ratio by applying the standard formula

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

and reducing the resulting fraction to a

1 \text{ in } N

form.

Recall the fundamental gradient formula

Gradient =

\frac{\text{Vertical Interval (VI)}}{\text{Horizontal Equivalent (HE)}}

Gradient measures the ratio of vertical elevation change to horizontal ground distance.

Calculate the ratio for the first measurement set (

20\text{ m}

VI and

200\text{ m}

HE)

\frac{20}{200} = \frac{1}{10} = 1 \text{ in } 10

Dividing both numerator and denominator by 20 simplifies the fraction to 1 in 10.

Calculate the ratio for the second measurement set (

50\text{ m}

VI and

1,000\text{ m}

HE)

\frac{50}{1000} = \frac{1}{20} = 1 \text{ in } 20

Dividing both numerator and denominator by 50 simplifies the fraction to 1 in 20.

Calculate the ratio for the third measurement set (

100\text{ m}

VI and

500\text{ m}

HE)

\frac{100}{500} = \frac{1}{5} = 1 \text{ in } 5

Dividing both numerator and denominator by 100 simplifies the fraction to 1 in 5.

Calculate the ratio for the fourth measurement set (

10\text{ m}

VI and

500\text{ m}

HE)

\frac{10}{500} = \frac{1}{50} = 1 \text{ in } 50

Dividing both numerator and denominator by 10 simplifies the fraction to 1 in 50.

Slope and Gradient Calculation

Question