Geek Challenge: A Place in the Sun

You are an engineer on site in Lebanon, Kansas. At sunrise on the vernal equinox, you hop in your hovercar and start driving directly toward the rising sun along the ground at a constant 60 mph. You continue driving in this way until the sun sets.

What are your coordinates when you stop driving?

Parameters
•    Coordinates of Lebanon, Kansas: 39°48′38″N 98°33′22″W
•    Vernal Equinox: September 22, 2018
•    Time of Sunrise: 7:22:43 am
•    Time of Sunset: 7:30:29 pm

Assumptions
•    You experience no change in elevation
•    Your hovercar has enough fuel to last the entire drive
 

Sun trajectory (source)

Bonus Questions
1.    Is there any non-zero constant velocity for which you will end up where you started?
2.    How can your solution be generalized for different Latitudes and times of the year?

Remember to state any additional simplifying assumptions you use in solving this problem! 

Submit responses to geekchallenge@dmcinfo.com by October 9, 2018.

Check out previous Geek Challenges.