题目描述
The Tower shows atall tower perched on the top of a rocky mountain. Lightning strikes, setting the building alight， and two people leap frnm the windows, head first and arms outstretched.
It is a scene of chaos and destruction.
There is a cone tower with base center at (0, 0, 0), base radius r and apex (0, 0, h) . At time 0 , a point located at ( x0 ，y0， z0) with velocity （vx,vy,vz）. What time will they collide? Here is the cone tower.
输入
The first line contains testcase number T (T≤1000), For each testcase the first line contains spaceseparated real numbers rand h (1≤r,h≤1000) the base radius and the cone height correspondingly.
For each testcase the second line contains three real numbers x0 ，y0， z0 (0≤|x0|,|y0|,z0≤1000). For each testcase the third line contains three real numbers vx,vy,vx (
). It is guaranteed that at time 0 the point is outside the cone and they will always collide.
输出
For each testcase print Case i: and then print the answer in one line, with absolute or relative error not exceeding 10-6
样例输入
复制样例数据
2 1 2 1 1 1 -1.5 -1.5 -0.5 1 1 1 1 1 -1 -1 -1
样例输出
Case 1: 0.3855293381 Case 2: 0.5857864376
/*
x=x0+vx*t;
y=y0+vy*t;
z=z0+vz*t;
sqrt(x*x+y*y)/r=(h-z)/h;
*/
#include<iostream>
#include<cmath>
using namespace std;
double x,y,z,vx,vy,vz;
double r,h;
int main()
{
int t;
cin>>t;
for(int k=1; k<=t; k++)
{
cin>>r>>h;
cin>>x>>y>>z;
cin>>vx>>vy>>vz;
double a=h*h*vx*vx+h*h*vy*vy-r*r*vz*vz;
double b=2*(h*h*x*vx+h*h*y*vy+h*vz*r*r-z*vz*r*r);
double c=x*x*h*h+y*y*h*h-(z-h)*(z-h)*r*r;
double res1=(-b+sqrt(b*b-4*a*c))*1.0/(2*a);
double res2=(-b-sqrt(b*b-4*a*c))*1.0/(2*a);
double res=999999999999.999;
if(res1>=0&&(z+vz*res1)>=0&&(z+vz*res1)<=h)
res=min(res,res1);
if(res2>=0&&(z+vz*res2)>=0&&(z+vz*res2)<=h)
res=min(res,res2);
printf("Case %d: %.12f\n",k,res);
}
return 0;
}