063. Schwarzschild Radius

Codeforces

IDCF10269063

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

The event horizon of a black hole, also known as the Schwarzschild radius, is the radius from a black hole at which even light can no longer escape. The formula to calculate the Schwarzschild radius of a given mass is $r_s = frac(2 G M, c^2)$. The value $G$ is the universal gravitational constant, which you should consider to be $6. 67 * 10^(-1)$ for this problem. $G$ is being given such a high value under the assumption that the masses being input will be incredibly large. The value of $M$ will be provided, and the value of $c$ is the speed of light, which you should consider to be $3 * 10^4$ for this problem. The value of $c$ is being decreased due to the incredibly low values that it normally produces. A single floating point value M that represents the mass of the object. The value of M will be between 0 and 1000000000. A single floating point value that represents the Schwarzschild radius of the object. Make sure to use the shortened values for $G$ and $c$ provided in the question, and not the more precise actual values. The reason that the values for $G$ and $c$ have been changed is that the use of their actual values causes such low floating point values that errors can occur, and handling such errors is not the goal of this problem. When actually calculating the event horizon, the real values of $G$ and $c$ should be used. ## Input A single floating point value M that represents the mass of the object. The value of M will be between 0 and 1000000000. ## Output A single floating point value that represents the Schwarzschild radius of the object. [samples] ## Note Make sure to use the shortened values for $G$ and $c$ provided in the question, and not the more precise actual values. The reason that the values for $G$ and $c$ have been changed is that the use of their actual values causes such low floating point values that errors can occur, and handling such errors is not the goal of this problem. When actually calculating the event horizon, the real values of $G$ and $c$ should be used.

**Definitions** Let $ M \in \mathbb{R} $ be the mass of the object, with $ 0 \leq M \leq 10^9 $. Let $ G = 6.67 \times 10^{-1} $ be the gravitational constant. Let $ c = 3 \times 10^4 $ be the speed of light. **Objective** Compute the Schwarzschild radius: $$ r_s = \frac{2 G M}{c^2} $$

API Response (JSON)

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