Final answer:
The student's task involves using vector addition to determine D'Artagnan the duck's resultant velocity given its airspeed and the tailwind, then calculating the ETA to Lake Canard. Furthermore, the student must adjust the duck's heading to maintain a NE path, and finally assess if D'Artagnan will be early or late.
Step-by-step explanation:
The student's question involves determining D'Artagnan the duck's resultant velocity when flying with an airspeed and heading on a breezy day with tail winds, and adjusting its heading to arrive at a specific destination without being blown off course. This falls under the category of vector addition and relative motion in kinematics.
A) Resultant Velocity and ETA
D'Artagnan flies at 20 m/s [NE] and there is a tailwind of 5 m/s [E 30° N]. To find the resultant velocity, we combine these two vectors using vector addition (typically done with trigonometric methods or a graphical approach).
Once we have the resultant velocity, we can calculate the expected arrival time (naively expected ETA) by dividing the distance to Lake Canard (2 km) by the resultant velocity's magnitude. The position relative to the lake would be determined based on this velocity and the time spent flying.
B) Corrected Heading
To determine which direction D'Artagnan should actually fly to compensate for the wind, we would adjust the original heading so that the tailwind corrects the duck's path to the desired NE direction. This involves more vector manipulation. Once we've determined the correct heading, we can then determine the time of arrival and compare it to the naively expected ETA to find out if D'Artagnan will be early or late.