TOJ 1320.Billiard

题目链接：http://acm.tju.edu.cn/toj/showp1320.html

1320. Billiard

Time Limit: 1.0 Seconds Memory Limit: 65536K
Total Runs: 315 Accepted Runs: 213 Multiple test files

In a billiard table with horizontal side a inches and vertical side b inches, a ball is launched from the middle of the table. After s > 0 seconds the ball returns to the point from which it was launched, after having made m bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angle A(measured from the horizontal), which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball.

Assume that the collisions with a side are elastic (no energy loss), and thus the velocity component of the ball parallel to each side remains unchanged. Also, assume the ball has a radius of zero. Remember that, unlike pool tables, billiard tables have no pockets.

Input

Input consists of a sequence of lines, each containing five nonnegative integers separated by whitespace. The five numbers are: a, b, s, m, and n, respectively. All numbers are positive integers not greater than 10000.

Input is terminated by a line containing five zeroes.

Output

For each input line except the last, output a line containing two real numbers (accurate to two decimal places) separated by a single space. The first number is the measure of the angle A in degrees and the second is the velocity of the ball measured in inches per second, according to the description above.

Sample Input

100 100 1 1 1
200 100 5 3 4
201 132 48 1900 156
0 0 0 0 0

Sample Output

45.00 141.42
33.69 144.22
3.09 7967.81

Source: Waterloo Local Contest Jun. 19, 1999

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反射问题，其实就是球在水平方向位移为a*m，竖直方向位移为b*n，用时为t，所以初始运动方向为ans=atan(1.0*sy/sx); 初速度为：v=(1.0*sy/s)/sin(ans);

#include <stdio.h>
#include <cmath>
int main(){int a,b,s,m,n;int sx,sy;double ans,v;while(~scanf("%d%d%d%d%d",&a,&b,&s,&m,&n)&&(a||b||s||m||n)){sx=a*m;sy=b*n;ans=atan(1.0*sy/sx);v=(1.0*sy/s)/sin(ans);printf("%.2lf %.2lf\n",ans*180/(acos(-1)),v);}
}