Convert Speed of sound at 20 degrees Celsius to Escape velocity (Earth)
Unit definitions
Speed of sound at 20 degrees Celsius
The speed of sound in air is $343.21\ \text{m/s}$ at 20 degrees Celsius.
Escape velocity (Earth)
The escape velocity is the minimum speed required to overcome the effects of gravity from the surface without falling back. The escape velocity of Earth is equal to $11.186\ \text{km/s}$.
How to convert Speed of sound at 20 degrees Celsius to Escape velocity (Earth)
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = \text{Speed}_{\text{Speed of sound₂₀}} \cdot 0.03068210262828535669586983729662078$$
Examples
Example 1
Convert $45.0\ \text{Speed of sound₂₀}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 45.0 \cdot 0.03068210262828535669586983729662078$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 1.380695$$
$$\therefore \ 45.0\ \text{Speed of sound₂₀} = 1.380695 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 2
Convert $65.0\ \text{Speed of sound₂₀}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 65.0 \cdot 0.03068210262828535669586983729662078$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 1.994337$$
$$\therefore \ 65.0\ \text{Speed of sound₂₀} = 1.994337 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 3
Convert $105.0\ \text{Speed of sound₂₀}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 105.0 \cdot 0.03068210262828535669586983729662078$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 3.221621$$
$$\therefore \ 105.0\ \text{Speed of sound₂₀} = 3.221621 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 4
Convert $150.0\ \text{Speed of sound₂₀}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 150.0 \cdot 0.03068210262828535669586983729662078$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 4.602315$$
$$\therefore \ 150.0\ \text{Speed of sound₂₀} = 4.602315 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 5
Convert $170.0\ \text{Speed of sound₂₀}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 170.0 \cdot 0.03068210262828535669586983729662078$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 5.215957$$
$$\therefore \ 170.0\ \text{Speed of sound₂₀} = 5.215957 \ \text{Escape Velocityₑₐᵣₜₕ}$$