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The terminal velocity equation provides a means to calculate the maximum velocity reached by a falling object when the upward force of air resistance equals the downward force of gravity. It can be expressed as vt = √2 m g/ρ A CD, where vt represents the terminal velocity, m is the mass of the object, g is the gravitational acceleration, ρ is the density of the medium through which the object is falling, A is the cross-sectional area of the object, and CD is the drag coefficient.
Practice problems
Problem #1
What is the terminal velocity of a 0.5 kg parachute bag thrown from a plane? Given the density of the air as 1.21 kg/m3, the cross-sectional area of the parachute bag as 0.10 m2, and the drag coefficient as 0.12. Take the value of gravitational acceleration as g = 9.81 m/s2.
Solution
Given data:
- Terminal velocity of a parachute bag, vt = ?
- Mass of a parachute bag, m = 0.5 kg
- Density of the air, ρ = 1.21 kg/m3
- Cross sectional area of a parachute bag, A = 0.10 m2
- Drag coefficient, CD = 0.12
- Gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- vt = √2 m g/ρ A CD
- vt = √(2 × 0.5 × 9.81)/(1.21 × 0.10 × 0.12)
- vt = √(9.81)/(0.0145)
- vt = √676.5517
- vt = 26.01 m/s
Therefore, the terminal velocity of a parachute bag is 26.01 m/s.
Problem #2
When a skydiver weighing 55 kg jumps from a helicopter, he reaches the terminal velocity after traveling a certain distance. Calculate the terminal velocity of the skydiver, considering the density of the air as 1.25 kg/m3, the cross-sectional area of the skydiver as 0.20 m2, and the drag coefficient as 0.70.
Solution
Given data:
- Mass of a skydiver, m = 55 kg
- Terminal velocity of a skydiver, vt = ?
- Density of the air, ρ = 1.25 kg/m3
- Cross sectional area of a skydiver, A = 0.20 m2
- Drag coefficient, CD = 0.70
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- vt = √2 m g/ρ A CD
- vt = √(2 × 55 × 9.81)/(1.25 × 0.20 × 0.70)
- vt = √(1079.1)/(0.175)
- vt = √6166.2857
- vt = 78.52 m/s
Therefore, the terminal velocity of a skydiver is 78.52 m/s.
Problem #3
A leaf with a mass of 0.05 kg is floating in the air and descending from a certain height, eventually reaching its terminal velocity “vt.” If the density of the air is 1.22 kg/m3, the cross-sectional area of the leaf is 0.05 m2, and the drag coefficient is 0.08, determine the value of the leaf’s terminal velocity.
Solution
Given data:
- Mass of a leaf, m = 0.05 kg
- Density of the air, ρ = 1.22 kg/m3
- Cross sectional area of a leaf, A = 0.05 m2
- Drag coefficient, CD = 0.08
- Terminal velocity of a leaf, vt = ?
- Assuming gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- vt = √2 m g/ρ A CD
- vt = √(2 × 0.05 × 9.81)/(1.22 × 0.05 × 0.08)
- vt = √(0.981)/(0.0048)
- vt = √204.375
- vt = 14.29 m/s
Therefore, the terminal velocity of a leaf is 14.29 m/s.
Problem #4
Calculate the terminal velocity of a 0.012 kg feather floating in the air. Given the density of the air as 1.20 kg/m3, the cross-sectional area of the feather as 0.02 m2, and the drag coefficient as 0.05. Take the value of gravitational acceleration as g = 9.81 m/s2.
Solution
Given data:
- Terminal velocity of a feather, vt = ?
- Mass of a feather, m = 0.012 kg
- Density of the air, ρ = 1.20 kg/m3
- Cross sectional area of a feather, A = 0.02 m2
- Drag coefficient, CD = 0.05
- Gravitational acceleration, g = 9.81 m/s2
Applying the formula:
- vt = √2 m g/ρ A CD
- vt = √(2 × 0.012 × 9.81)/(1.20 × 0.02 × 0.05)
- vt = √(0.2354)/(0.0012)
- vt = √196.1666
- vt = 14 m/s
Therefore, the terminal velocity of a feather is 14 m/s.
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Related
- Free fall equation
- Air resistance formula
- Terminal velocity equation
- Gravity equation
- Inertia formula
- Acceleration formula
- Momentum equation
- Mass formula
- Velocity formula
- Pressure equation
- Kinematic equations
- Friction equation
External links
- Terminal Velocity – NASA (.gov)
- 3 Ways to Calculate Terminal Velocity – wikiHow
- Terminal Velocity Calculator – Omni Calculator
- Terminal Velocity Definition, Formula & Examples – Study.com
- 6.7: Drag Force and Terminal Speed – Physics LibreTexts
- Drag Force and Terminal Speed – BCcampus Pressbooks
- Terminal velocity – Wikipedia
- Terminal Velocity Calculator – GIGACalculator.com
- Terminal Velocity – HyperPhysics Concepts
- How to Calculate Terminal Velocity – Sciencing
- How can I calculate the terminal velocity of a falling object? – Quora
- The Difference Between Terminal Velocity and Free Fall – ThoughtCo
- 6.4 Drag Force and Terminal Speed – UCF Pressbooks
- Is there a way to calculate the time taken by a falling object to reach terminal velocity? – Physics Stack Exchange
- Terminal Velocity – an overview – ScienceDirect
- Terminal Velocity: Definition, Formula, Speed, Calculate – Vaia
- Drag Force and Terminal Velocity – AK Lectures
- Drag – University of Tennessee, Knoxville
- Terminal Velocity Calculator – CalcTool
- Terminal Velocity Calculator – Calculator Academy
- Terminal Velocity Calculator – GoSkydive
- What is Terminal Velocity? How Do We Find It? – Flipping Physics
- Terminal Velocity of a Human, Free Fall and Drag Force – Owlcation
- Terminal velocity | Definition, Examples, & Facts – Britannica
- Terminal Velocity Calculator – Calculator-online.net
- Which is the equation for terminal velocity? – Brainly
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