An alternative solution to the Boat heading across the river problem

Last time I set up two equations in two unknowns (theta and v), eliminated v and then had Wolframalpha solve for theta.

Another approach, illustrated below, gives an analytical solution for v, which can then get plugged in to get theta.
I mentioned this as a possible solution in class today but hadn't worked it out.
Here it is:


Folks in my TuTh class seemed at least intrigued by the log-log linearization of the period mass data and adjusting the "Mass of the tray" parameter until they get a perfect straight line. Hooray!