Convert Speed of sound rounded to Escape velocity (Earth)
Unit definitions
Speed of sound rounded
The speed of sound is frequently rounded to $340\ \text{m/s}$ in introductory physics calculations.
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 rounded to Escape velocity (Earth)
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = \text{Speed}_{\text{Speed of sound}} \cdot 0.03039513677811550151975683890577508$$
Examples
Example 1
Convert $40.0\ \text{Speed of sound}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 40.0 \cdot 0.03039513677811550151975683890577508$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 1.215805$$
$$\therefore \ 40.0\ \text{Speed of sound} = 1.215805 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 2
Convert $60.0\ \text{Speed of sound}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 60.0 \cdot 0.03039513677811550151975683890577508$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 1.823708$$
$$\therefore \ 60.0\ \text{Speed of sound} = 1.823708 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 3
Convert $105.0\ \text{Speed of sound}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 105.0 \cdot 0.03039513677811550151975683890577508$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 3.191489$$
$$\therefore \ 105.0\ \text{Speed of sound} = 3.191489 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 4
Convert $150.0\ \text{Speed of sound}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 150.0 \cdot 0.03039513677811550151975683890577508$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 4.559271$$
$$\therefore \ 150.0\ \text{Speed of sound} = 4.559271 \ \text{Escape Velocityₑₐᵣₜₕ}$$
Example 5
Convert $160.0\ \text{Speed of sound}$ to $\text{Escape Velocityₑₐᵣₜₕ}$.
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 160.0 \cdot 0.03039513677811550151975683890577508$$
$$\text{Speed}_{\text{Escape Velocityₑₐᵣₜₕ}} = 4.863222$$
$$\therefore \ 160.0\ \text{Speed of sound} = 4.863222 \ \text{Escape Velocityₑₐᵣₜₕ}$$