Terminal Velocity Calculator

Calculate Terminal Velocity

Mass (m):

kg g lb

Cross-Sectional Area (A):

m² cm² ft²

Drag Coefficient (C_d):

Fluid Density (ρ):

kg/m³ g/cm³ lb/ft³

Gravitational Acceleration (g):

m/s² ft/s²

Calculate Example

How to Calculate Terminal Velocity

Terminal velocity is a crucial concept in physics, representing the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. Understanding how to calculate terminal velocity is essential for solving problems involving falling objects, fluid dynamics, and various scenarios in physics and engineering.

What is the Formula?

The formula for calculating terminal velocity is:

\[ v_t = \sqrt{\frac{2mg}{\rho A C_d}} \]

Where:

• \(v_t\) is the terminal velocity
• \(m\) is the mass of the object
• \(g\) is the acceleration due to gravity
• \(\rho\) is the density of the fluid through which the object is falling
• \(A\) is the projected area of the object (cross-sectional area)
• \(C_d\) is the drag coefficient

What are the calculation steps?

1. Determine the mass of the object (m).
2. Find the acceleration due to gravity (g) for the location.
3. Determine the density of the fluid (ρ) through which the object is falling.
4. Calculate or measure the projected area (A) of the object.
5. Find the drag coefficient (C_d) for the object's shape.
6. Apply the formula: \(v_t = \sqrt{\frac{2mg}{\rho A C_d}}\)
7. Simplify and solve for v_t.

Example Calculation

Let's calculate the terminal velocity for a skydiver:

Given:

• Mass of skydiver (m) = 70 kg
• Acceleration due to gravity (g) = 9.8 m/s²
• Density of air (ρ) = 1.225 kg/m³
• Projected area of skydiver (A) = 0.5 m²
• Drag coefficient of skydiver (C_d) = 0.7

Step 1: Plug the values into the formula

\(v_t = \sqrt{\frac{2 \times 70 \times 9.8}{1.225 \times 0.5 \times 0.7}}\)

Step 2: Simplify and calculate

\(v_t = \sqrt{\frac{1372}{0.42875}} = \sqrt{3200} \approx 56.57 \text{ m/s}\)

Therefore, the terminal velocity of the skydiver is approximately 56.57 m/s or 203.65 km/h.

Diagram of Terminal Velocity

The following diagram illustrates the concept of terminal velocity:

This diagram shows an object (red circle) falling through a fluid (light blue rectangle). The blue arrow represents the upward drag force, while the green arrow represents the downward gravitational force. At terminal velocity, these forces are equal in magnitude but opposite in direction, resulting in no net acceleration and a constant velocity.