I just realized I used the wrong equation. I am not sure if there was a typo, but the calculation of s should give some number slightly greater than 5, not 3.53…
Looking again, the correct equation is below:
It appears to need a numeric solution. I was able to quickly iterate on a solution which makes sense.
manipulate to solve for s (as a function of s):
s=2asinh*(h/2a)-sqrt(s^2-v^2)+s
Start by assuming s=5.
Iteration 1:
s=2150sinh(3.53553/(2*150))-sqrt(5^2-3.53553^2)+5
s=5.000074
Iteration 2:
s=2150sinh(3.53553/(2*150))-sqrt(5.000074^2-3.53553^2)+5.000074
s=5.00004337
Iteration 3:
s=2150sinh(3.53553/(2*150))-sqrt(5.00004337^2-3.53553^2)+5.00004337
s=5.00005606
…
My numeric method could probably be improved upon, but the numbers seem to be reasonable.