UVA10387 Billiard
2014-07-19 16:56
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Description
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
Sample Output
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 题目的意思就是在一张长a宽b的桌子正中心有一个球,和水平方向以某个夹角,某个速度打出,在s秒后回到原来位置并且 和水平方向撞了m次,垂直方向撞了n次,, 给出桌子长宽,时间,水平碰的次数,垂直碰的次数。。。求夹角和速度。。。 就是根据长宽,时间和碰的次数,算出水平运动了多远,垂直运动了多久,再用三角函数求角度和速度。。 AC代码:#include<stdio.h> #include<cmath> int main () { double a,b,s,m,n; double cd,rd,d,de; double crate,rrate,rate; while (scanf("%lf%lf%lf%lf%lf",&a,&b,&s,&m,&n)) { if(a == 0 && b == 0 && s == 0 && m == 0 && n == 0) break; cd = m * a; rd = n * b; d = sqrt(cd * cd + rd *rd); rate = d /s; de = atan(rd/cd); de = de * 180 / acos(-1); printf("%.2lf %.2lf\n",de,rate); } }
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