H

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <iostream>
 6 using namespace std;
 7 
 8 #define eps 1e-8
 9 #define pie 3.14159265
10 
11 struct point
12 {
13     double x, y;
14 }p, s, O;
15 double vp, vs, r, dis, alpha;
16 
17 double square( double x ) {
18     return x * x;
19 }
20 
21 double Dist( point p1, point p2 ) {
22     return sqrt( square( p1.x - p2.x ) + square( p1.y - p2.y ) );
23 }
24 
25 point rotate( double T ) {
26     double theta = T * vp / dis;
27     theta += alpha;
28     point newp;
29     newp.x = cos( theta ) * dis;
30     newp.y = sin( theta ) * dis;
31     return newp;
32 }
33 
34 int main()
35 {
36 //
37 //    freopen("haha.txt", "r", stdin);
38 //    freopen("out.txt", "w", stdout);
39 
40     double L, R, mid, d1, d2, cxc, T, theta1, theta2, theta3, dc, ans;
41 
42     while(scanf("%lf%lf%lf", &s.x, &s.y, &vs) == 3) {
43         
44         scanf("%lf%lf%lf%lf", &p.x, &p.y, &vp, &r);
45 
46 
47         O.x = 0.0; O.y = 0.0;
48         dis = Dist( O, p );
49         alpha = atan2( p.y, p.x );
50 
51         L = 0.0; R = 100000.0; ans = R;
52         while( ( R - L ) > eps ) {
53             mid = ( L + R ) / 2;
54             point newp = rotate( mid );
55 
56             d1 = Dist( s, O );
57             theta1 = acos( r / d1 );
58 
59             d2 = Dist( newp, O );
60             theta2 = acos( r / d2 );
61 
62             dc = newp.x * s.x + newp.y * s.y;
63             theta3 = acos( dc / ( d1 * d2 ) );
64 
65             if( theta1 + theta2 > theta3 ) {
66                 d1 = Dist( s, newp );
67                 T = d1 / vs;
68             }
69             else {
70                 T = 0.0;
71                 cxc = sqrt( d1 * d1 - r * r );
72                 T += cxc / vs;
73                 cxc = sqrt( d2 * d2 - r * r );
74                 T += cxc / vs;
75                 theta3 = theta3 - theta1 - theta2;
76                 T += r * theta3 / vs;
77             }
78 
79             if( ( mid - T ) >= eps ) {
80                 R = mid - eps;
81                 ans = min( ans, mid );
82             }
83             else L = mid + eps;
84         }
85         printf("%.2lf
", ans );
86 
87     }
88     return 0;
89 }