Tears in rain

2019 is the death year of Roy Batty, the leader of the renegade Nexus-6
replicants of the cult film Blade Runner. Also, 2019 has been the death
year of Rutger Hauer, the actor that so brillianty played the role of
Roy Batty on film. That sad coincidence deserves a problem.

0.67 Roy Batty has died. A starship will transport his body from the
Tannhäuser Gate to the shoulder of Orion. Assume a two-dimensional
universe, centered at the middle of Orion. The shoulder of Orion orbits
around its center as a circumference. Its position as a function of the
time t ≥ 0 is (Rcos t, Rsin t). The Tannhäuser Gate is located at
(T_(x), T_(y)). The starship can freely change its speed and direction,
with just one restriction: a maximum absolute speed of S.

0.32

[image]

Your task is to compute the minimum time to transport Roy’s body from
the Tannhäuser Gate to the shoulder of Orion. Consider all objects as
points.

Input

Input consists of several cases, each with four real numbers R, T_(x),
T_(y) and S. You can assume 0 < R < S.

Output

For each case, print the answer with four digits after the decimal
point. The input cases have no precision issues.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:01:10.130Z

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