calculus and analysis – Findroot and arc length,similar situation but does not work

In another problem I was presented with this situation
It is to find the arc length of the curve

  x = 50 (1 - Cos(t)) + 50 (2 - t) Sin(t);
  y = 50 Sin(t) + 50 (2 - t) Sin(t);

from t=0 to t =tmax , in such a way that the length is 100 units

which works perfectly

FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 1})
{tmax -> 0.832919}

, then an error was discovered in the second equation and I tried to do the same but it does not work.

  x = 50 (1 - Cos(t)) + 50 (2 - t) Sin(t);
  y = 50 Sin(t) + 50 (2 - t) Cos(t);
  FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 1})

  (*FindRoot::nlnum: The function value {False} is not a list of numbers with dimensions {1} at {tmax} = {1.}.*)

I changed it to 2 because at t=2 100 units are produced but it does not work. I don’t understand why

FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 2})