I took these photos from the north end of Dangerfield Island (38 50 00.21 N / 77 02 28.72 W). There is parking at the Washington Sailing Marina – 1 Marina Dr, Alexandria, VA 22314. When I took these the lot was open from 6AM-Midnight.
I anchored the left side of the shot on the Washington Memorial so anyone looking at the photo would know what airport it was.
I set my focus point on the actual take off point and pulled the trigger on a 13 second exposure about three seconds before the plane took off.
You will need to practice on a couple of flights to get the timing right. Make sure to take a bunch of exposures because all the different aircraft types have different take off profiles.