HDU 1155 Bungee Jumping（纯物理题）
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.
题意：一个人想要从桥上逃生，现在他有一条有弹性的绳子，他将自己绑在绳子的一端，绳子的另一端绑在桥上，然后跳下去，那么我们需要判断一下他跳下去之后会发生什么，可能有三种情况：
（1）：绳子的长度本身就比桥的高度要长，那么他肯定能落地，只需要判断一下他落地的速度就可以了，如果速度大于10则撞死（Killed by the impact.），否则安全着陆（James Bond survives.）；
（2）：绳子的长度本身没有桥的高度长，经过下坠时的拉伸变长，当绳子达到最长时如果还没有桥的高度长，他就会被困在空中（Stuck in the air.）；
（3）：拉伸过的长度大于等于桥的高度了，那么只需要判断他落地时的速度是否大于10。
#include<stdio.h> #include<math.h> const double g=9.81; int main () { double k, l, s, w, v, ll, a; while (scanf("%lf%lf%lf%lf", &k, &l, &s, &w), k+l+s+w) { if (l >= s) { v = sqrt(2*g*s); ///落地时只有重力势能（1/2*w*v*v = w*g*s） if (v > 10) printf("Killed by the impact.\n"); else printf("James Bond survives.\n"); } else { a = 2*w*g*s; ///当绳子拉伸到最长时，重力势能等于弹性势能（1/2*k*ll*ll = w*g*s） ll = sqrt(a / k); ///ll是绳子被拉伸的长度 if (ll+l < s) printf("Stuck in the air.\n"); else { a = w*g*s - 0.5*k*(s-l)*(s-l); v = sqrt(2*a / w); ///拉伸后再落地时有弹性势能和重力势能，根据动能定理（1/2*w*v*v + 1/2*k*(s-l)*(s-l) = w*g*s） if (v > 10) printf("Killed by the impact.\n"); else printf("James Bond survives.\n"); } } } return 0; }
