All-terrain vehicle#244
The all-terrain vehicle must travel from the starting point to the finish point across the steppe, where there is a desert area. The desert area is a wedge-shaped region on the plane, defined by two rays originating from the origin. One ray is directed upwards along the axis, and the other is in the 1st quadrant, forming an angle with the first ray. The vehicle can travel through the desert at speed V_1, and through the steppe at speed V_0 (V_0 \geq V_1). What is the minimum time required for the vehicle to travel from point to point ?
The single line of input contains real numbers: X_S, Y_S, X_F, Y_F, , V_0, V_1, which represent the coordinates of point S(X_S, Y_S), the coordinates of point F(X_F, Y_F), the angle at the vertex of the wedge (in radians), and the vehicle's speeds in the steppe and in the desert.
Output a single real number — the minimum time , accurate to three decimal places.
-1000 < X_S < 0 < X_F < 1000; -1000 < Y_S, Y_F < 1000; both points and are outside the desert and not on its boundary; the segment intersects the desert.
\pi/180 < \varphi < \pi/4; V_1 \leq V_0 \leq 4V_1; 0.1 \leq V_1 \leq 5.
Example 1