通过物理公式计算特工从桥上使用不同长度和强度的蹦极绳跳下的生存几率。涉及自由落体、弹力和能量守恒原理。
http://acm.hdu.edu.cn/showproblem.php?pid=1155
Bungee Jumping
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 1118 Accepted Submission(s): 473
Problem Description
Once again, James Bond is fleeing from some evil people who want to see him dead. Fortunately, he has left a bungee rope on a nearby highway bridge which he can use to escape from his enemies. His plan is to attach one end of the rope to the bridge, the other end of the rope to his body and jump off the bridge. At the moment he reaches the ground, he will cut the rope, jump into his car and be gone.
Unfortunately, he had not had enough time to calculate whether the bungee rope has the right length, so it is not clear at all what is going to happen when he jumps off the bridge. There are three possible scenarios:
The rope is too short (or too strong), and James Bond will never reach the ground.
The rope is too long (or too weak), and James Bond will be going too fast when he touches the ground. Even for a special agent, this can be very dangerous. You may assume that if he collides at a speed of more than 10 m/s, he will not survive the impact.
The rope's length and strength are good. James Bond touches the ground at a comfortable speed and can escape.
As his employer, you would like to know whether James Bond survives or whether you should place a job ad for the soon-to-be vacant position in the local newspaper. Your physicists claim that:
The force with which James is pulled towards the earth is
9.81 * w,
where w is his weight in kilograms and 9.81 is the Earth acceleration in meters over squared seconds.
Mr. Bond falls freely until the rope tautens. Then the force with which the bungee rope pulls him back into the sky depends on the current length of the rope and is
k * Δl,
where Δl is the difference between the rope's current length and its nominal, unexpanded length, and k is a rope-specific constant.
Given the rope's strength k, the nominal length of the rope l in meters, the height of the bridge s in meters, and James Bond's body weight w, you have to determine what is going to happen to our hero. For all your calculations, you may assume that James Bond is a point at the end of the rope and the rope has no mass. You may further assume that k, l, s, and w are non-negative and that s < 200.
The input contains several test cases, one test case per line. Each test case consists of four floating-point numbers (k, l, s, and w) that describe the situation. Depending on what is going to happen, your program must print "Stuck in the air.", "Killed by the impact.", or "James Bond survives.". Input is terminated by a line containing four 0s, this line should not be processed.
Unfortunately, he had not had enough time to calculate whether the bungee rope has the right length, so it is not clear at all what is going to happen when he jumps off the bridge. There are three possible scenarios:
The rope is too short (or too strong), and James Bond will never reach the ground.
The rope is too long (or too weak), and James Bond will be going too fast when he touches the ground. Even for a special agent, this can be very dangerous. You may assume that if he collides at a speed of more than 10 m/s, he will not survive the impact.
The rope's length and strength are good. James Bond touches the ground at a comfortable speed and can escape.
As his employer, you would like to know whether James Bond survives or whether you should place a job ad for the soon-to-be vacant position in the local newspaper. Your physicists claim that:
The force with which James is pulled towards the earth is
9.81 * w,
where w is his weight in kilograms and 9.81 is the Earth acceleration in meters over squared seconds.
Mr. Bond falls freely until the rope tautens. Then the force with which the bungee rope pulls him back into the sky depends on the current length of the rope and is
k * Δl,
where Δl is the difference between the rope's current length and its nominal, unexpanded length, and k is a rope-specific constant.
Given the rope's strength k, the nominal length of the rope l in meters, the height of the bridge s in meters, and James Bond's body weight w, you have to determine what is going to happen to our hero. For all your calculations, you may assume that James Bond is a point at the end of the rope and the rope has no mass. You may further assume that k, l, s, and w are non-negative and that s < 200.
The input contains several test cases, one test case per line. Each test case consists of four floating-point numbers (k, l, s, and w) that describe the situation. Depending on what is going to happen, your program must print "Stuck in the air.", "Killed by the impact.", or "James Bond survives.". Input is terminated by a line containing four 0s, this line should not be processed.
Sample Input
350 20 30 75 375 20 30 75 400 20 30 75 425 20 30 75 450 20 30 75 400 20 30 50 400 20 30 80 400 20 30 85 0 0 0 0
Sample Output
Killed by the impact. James Bond survives. James Bond survives. James Bond survives. Stuck in the air. Stuck in the air. James Bond survives. Killed by the impact.
Source
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题意：
特工从高为 s 的的桥上跳下，绳子的长度 l ，绳子弹性系数 k ，特工体重 w 。
问一些情况能否发生。
思路：
考虑绳长和桥的高度，利用的公式：
弹力的公式，功能关系，重力和弹力做功。
恰好留在空中的条件：重力和拉力相同的时候，计算绳长的变化，计算出二者做功的差值。
直接看代码吧。
参考Code：
//用的都是高中的物理知识.
//保佑我 1A 昂，就会这一个，
//敲了一个多钟头曲折的 AC 路，
#include<cstdio>
#include<cstring>
#include<cmath>
typedef double DB;
const int MYDD = 1103;
const DB g=9.81;//重力加速度
DB v; //到达地面的速度
DB a,b,c;//二次函数的系数
DB cl;//绳长变化
int flag=1;//标记不回到空中
int main() {
int dd=0;
DB k,l,s,w;
while(1) {
scanf("%lf%lf%lf%lf",&k,&l,&s,&w);
if(!(k||l||s||w)) break;
a=k,b=-2*w*g,c=-2*w*g*l;
if(l>=s) {//绳子太长或刚刚好做自由落体
v=sqrt(2.0*g*s);
} else {//绳子太短 l < s
cl=s-l;//绳子增加的长度
DB Ww=w*g*s;//重力做功
DB Wl=k*cl*cl/2.0;//绳子做功
DB Wwl=Ww-Wl;//差值
if(Wwl<0) {
flag=0;
} else {
v=sqrt(2.0*Wwl/w);
}
}
if(flag) {
if(v<=10.0) puts("James Bond survives.");
else puts("Killed by the impact.");
} else {
puts("Stuck in the air.");
}
}
return 0;
}
/* By: Shyazhut */
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