067. Tangential Velocity

Codeforces

IDCF10269067

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

When an object is rotating around a central point in circular motion, a force called centripetal force exists. Centripetal force is the force that pulls the object towards the center, preventing it from flying off in a straight line. An equation exists to relate the centripetal force $F_c$, the mass of the object $m$, the tangential velocity $v$, and the radius of the circle $r$. This equation is represented as follows: $F_c = frac(m v^2, r)$. To solve this problem, you will be given the centripetal force, the mass of the object, and the radius of the rotation. With this information, determine the tangential velocity of the moving object. The first line contains three space-separated floating point values that represent the centripetal force, the mass of the object, and the radius of the rotation respectively. Output a single floating point value that represents the tangential velocity of the movement. ## Input The first line contains three space-separated floating point values that represent the centripetal force, the mass of the object, and the radius of the rotation respectively. ## Output Output a single floating point value that represents the tangential velocity of the movement. [samples]

**Definitions** Let $ F_c \in \mathbb{R}^+ $ be the centripetal force, let $ m \in \mathbb{R}^+ $ be the mass of the object, let $ r \in \mathbb{R}^+ $ be the radius of circular motion, let $ v \in \mathbb{R}^+ $ be the tangential velocity. **Constraint** The physical relationship holds: $$ F_c = \frac{m v^2}{r} $$ **Objective** Given $ F_c $, $ m $, and $ r $, compute: $$ v = \sqrt{\frac{F_c \cdot r}{m}} $$

API Response (JSON)

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