https://vjudge.net/contest/386568#problem/K
Zhang3 a participant of IPhO (Immortal Physics Olympiad). The
0th0th problem in the contest is as follows.
There are two balls that weigh aa kg and bb kg respectively. They can be regarded as particles in this problem, as they are small enough. At the very beginning (i.e. t=0t=0), the distance between two balls is dd km, and both of them are not moving.
Assuming that only gravitation works in this system (no other objects or other forces considered). The two balls has started moving since t=0t=0. Your task is to calculate the distance between them when t=t0t=t0 (s).
Help Zhang3 solve the problem!
The following information might help when solving the problem.
- Universal gravitation formula: F=G⋅m1⋅m2/r2F=G⋅m1⋅m2/r2
- Gravitational constant: G=6.67430×10−11m3/(kg⋅s2)G=6.67430×10−11m3/(kg⋅s2)
There are two balls that weigh aa kg and bb kg respectively. They can be regarded as particles in this problem, as they are small enough. At the very beginning (i.e. t=0t=0), the distance between two balls is dd km, and both of them are not moving.
Assuming that only gravitation works in this system (no other objects or other forces considered). The two balls has started moving since t=0t=0. Your task is to calculate the distance between them when t=t0t=t0 (s).
Help Zhang3 solve the problem!
The following information might help when solving the problem.
- Universal gravitation formula: F=G⋅m1⋅m2/r2F=G⋅m1⋅m2/r2
- Gravitational constant: G=6.67430×10−11m3/(kg⋅s2)G=6.67430×10−11m3/(kg⋅s2)
InputThe first line of the input gives the number of test cases T(1≤T≤100)T(1≤T≤100). TT test cases follow.
For each test case, the only line contains four integers a,b,d,t0(1≤a,b,d,t0≤100)a,b,d,t0(1≤a,b,d,t0≤100), representing the mass of the two balls, the initial distance between them, and how much time the balls move.
It is guaranteed that two balls will not collide within (t0+1)(t0+1) seconds.
OutputFor each test case, print a line with a real number xx, representing that the distance is xx km.
Your answers should have absolute or relative errors of at most 10−610−6.
Sample Input
3 1 2 3 4 7 73 7 68 100 100 1 100
Sample Output
2.99999999999999999982 6.99999999999999974807 0.99999999999993325700
水题：只受万有引力 影响极小 不足精度
代码：
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