Terminal Velocity

Problem #74

Tags: physics

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In the previous problem, we observed the effects of air resistance on an object's trajectory. Let us recall the equation to approximate the Linear Drag on a sphere traveling through a viscous fluid:

$$ \huge F_{d} = -6 \pi \cdot \eta \cdot r \cdot \text{v} $$

Where

We can see that the drag force is directly proportional to the velocity. That is, if the object is traveling 2x faster, then the force of air resistance will also be 2x greater. This means an object in free-fall under constant effect of gravity will continuously accelerate until the force of air resistance prevents any further acceleration. This maximum speed that an obect can experience in free-fall is called its Terminal Velocity.

Problem Statement

Let's imagine we have some object with mass m (in kg) and radius r in freefall through the air, which has viscosity η. What is the Terminal Velocity of the object?
Assume acceleration due to gravity is constant g = -9.8 m/s^2

Input Data
First line will be Q, the quantity of testcases.
Q lines will then follow, each having a single testcase in the format m r η.

Answer
Should consist of Q space-separated values, being the terminal velocity of the object described in each testcase, in meters per second.
Error should be less than 1e-6.

Example

input data
1
1 2 3

answer
86.651025
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