Final answer:
Without the provided figure, it is not possible to determine the exact direction of the syncline plunge, but generally, the plunge direction points to where beds tilt downwards. A syncline dips towards the youngest rocks, and without a map or depicted arrows, one cannot confidently detail the plunge orientation.
Step-by-step explanation:
The main answer to the question on the direction in which the syncline is plunging cannot be confidently provided without a figure that explicitly shows the orientation and plunge direction of the syncline. However, general knowledge about synclines indicates that the plunge direction is where the beds point downwards. If you have an image or a map where the youngest rocks appear to converge towards a point, the syncline is plunging towards that point. If there's a symbol that indicates the plunge with an arrow, the direction the arrow points to gives the plunge direction.In the given example, if rocks become older as you move northwest, then on a regional scale, the rocks are dipping towards the southeast. Dip direction is perpendicular to the strike of the layers and is always down the steepest gradient. This orientation information can usually be gathered from geological maps that come with a legend indicating these features.To answer the other example question, if a river is flowing from southwest to northeast, and a boat that moves at a velocity of 13 m/s wants to head due east but account for a current moving at 7.1 m/s, it would need to compensate for the southwest-northeast flow. The conclusion is that specific information and numeric values would be required to calculate the exact direction and angle.