# Relativity | CodeChef Solution

Hello coders, today we are going to solve Relativity CodeChef Solution whose Problem Code is RELATIVE.

In Chefland, the speed of light is c m/s, and acceleration due to gravity is g m/s2.

Find the smallest height (in meters) from which Chef should jump such that during his journey down only under the effect of gravity and independent of any air resistance, he achieves the speed of light and verifies Einstein’s theory of special relativity.

Assume he jumps at zero velocity and at any time, his velocity (v) and depth of descent (H) are related as

v2 = 2⋅gH.

## Input

• The first line contains an integer T, the number of test cases. Then the test cases follow.
• Each test case contains a single line of input, two integers g, c.

## Output

For each test case, output in a single line the answer to the problem. We can show that under the constraints, the answer is an integer.

## Constraints

• 1 ≤ T ≤ 5⋅103
• 1 ≤ g ≤ 10
• 1000 ≤ c ≤ 3000
• 2⋅g divides c2.

Subtask #1 (100 points): Original constraints

Sample Input

``````3
7 1400
5 1000
10 1000``````

Sample Output

``````140000
100000
50000``````

## Explanation

Test Case 1: For Chef to achieve the speed of light, the minimum height required is c2/2⋅g = 1400⋅1400/14 = 140000 meters.

Test Case 3: For Chef to achieve the speed of light, the minimum height required is c2/2⋅g = 1000⋅1000/20 = 50000 meters.

## Solution – Relativity

### C++

```#include <iostream>
using namespace std;

int main() {
long t; cin >> t;
while(t--){
long g,c;
cin >> g >> c;
long ans = ((c*c)/(2*g));
cout << ans << "\n";
}
return 0;
}
```

### Python

```# cook your dish here
T = int(input())
for i in range(T):
g, c = map(int, input().split())
result = (c**2) // (2*g)
print(result)```

### Java

```/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
class Codechef
{
public static void main (String[] args) throws java.lang.Exception
{
Scanner sc = new Scanner(System.in);
long t = sc.nextInt();
while(t-->0){
long g,c;
g = sc.nextInt();
c = sc.nextInt();
long ans = (c*c/(2*g));
System.out.println(ans);
}
}
}
```

Disclaimer: The above Problem (Relativity) is generated by CodeChef but the Solution is Provided by CodingBroz. This tutorial is only for Educational and Learning Purpose.