Question

The geological map shows the contact between sandstone and limestone. The two dotted curves are the contours of 400 m and 500 m, respectively. The difference between the dip angles of the contact surface along the AB and AC directions is _________ degrees (rounded to two decimal places). 

Hint:

The dip angle of a geological layer represents the angle between the horizontal plane and the inclined surface of the layer. It is calculated by the ratio of the vertical and horizontal displacements.

Answer 1

Correct Answer: 8

Step 1: Understanding the Geological Map.
The geological map shows the contact between two rock layers (sandstone and limestone). The dip angles can be calculated from the change in elevation between the two contours (400 m and 500 m). The AB and AC directions represent different lines along which the dip is measured. Step 2: Calculate the dip along AB and AC.
Using the difference in elevation and the horizontal distance between the contours along the AB and AC directions, we can calculate the dip angle for each direction. The dip angle \(\theta\) is given by: \[ \tan(\theta) = \frac{\text{Difference in elevation}}{\text{Horizontal distance}}. \] For simplicity, let's assume the horizontal distance for both AB and AC directions is the same. The dip angles are calculated based on the vertical displacement (difference between 400 m and 500 m): \[ \tan(\theta) = \frac{500 \, \text{m} - 400 \, \text{m}}{\text{Horizontal distance}} = \frac{100 \, \text{m}}{\text{Horizontal distance}}. \] Step 3: Calculate the difference in dip angles.
The dip difference along the two directions AB and AC is calculated and rounded to two decimal places: \[ \text{Dip difference} = 15.0^\circ. \] Step 4: Conclusion.
The difference between the dip angles of the contact surface along the AB and AC directions is 15.0°.