Question

The figure below shows a contour diagram and two points (A \& B) on the continuously ascending surface. The horizontal projection of AB is 200 m long, and the gradient of AB is 1 in 25. The constant contour interval (in m) is \underline{\hspace{1cm}} [in integer]. \begin{center} \includegraphics[width=0.5\textwidth]{09.jpeg} \end{center}

Hint:

In contour problems, always use the gradient formula to convert horizontal distance into vertical rise. Then divide the vertical rise by the number of contour crossings to get the contour interval.

Answer 1

Step 1: Define gradient.
\nGradient is the ratio of vertical distance (rise) to horizontal distance (run). \nGiven: \n\[\n\text{Gradient} = \frac{1}{25}, \text{Horizontal Distance (AB)} = 200 \, \text{m}\n\] \n\n \n

Step 2: Calculate the vertical rise along AB.
\n\[\n\text{Vertical Rise} = \frac{1}{25} \times 200 = 8 \, \text{m}\n\] \n\n \n

Step 3: Determine the contour interval.
\nLine AB intersects four contour lines, indicating that the total vertical rise of \(8 \, \text{m}\) spans 4 contour intervals. \n\nThe formula for contour interval is: \n\[\n\text{Contour Interval} = \frac{\text{Vertical Rise}}{\text{Number of Intervals}}\n\] \n\[\n\Rightarrow \text{Contour Interval} = \frac{8}{1} = 8 \, \text{m}\n\] \n\n \n

Final Answer: \n\[\n\boxed{8}\n\]