I solved this problem as a differential equation. I’ve just realized that the equations above describe a straight line. A tangent to the 1/m circle. The duck moves in a straight line. I found a more complicated way of solving what could have been a simple problem.
V’z abg fher vs jr’er raqvat hc jvgu gur fnzr fgenvtug yvar gubhtu? Znlor zl frg bs genafpraqragny rdhngvbaf unf gur fvzcyr fbyhgvba bs gur gnatrag, juvpu V’ir bireybbxrq, ohg V guvax gur natyr bs gur yvar j.e.g. gur pvepyr bs enqvhf 1/z fubhyq qrcraq ba gur png’f fcrrq.
I solved this problem as a differential equation. I’ve just realized that the equations above describe a straight line. A tangent to the 1/m circle. The duck moves in a straight line. I found a more complicated way of solving what could have been a simple problem.
V’z abg fher vs jr’er raqvat hc jvgu gur fnzr fgenvtug yvar gubhtu? Znlor zl frg bs genafpraqragny rdhngvbaf unf gur fvzcyr fbyhgvba bs gur gnatrag, juvpu V’ir bireybbxrq, ohg V guvax gur natyr bs gur yvar j.e.g. gur pvepyr bs enqvhf 1/z fubhyq qrcraq ba gur png’f fcrrq.