**Air resistance formula**, also known as the drag force formula, calculates the force experienced by an object moving through a fluid medium, such as air. It is represented by the equation F_{D} = ½ × ρ A C_{D} v^{2}, where F_{D} is the drag force, ρ is the density of the fluid, A is the cross-sectional area of the object, C_{D} is the drag coefficient, and v is the velocity of the object.

## Practice problems

### Problem #1

Calculate the air resistance force acting on a feather that is falling with a velocity of 8 m/s. Given the density of the air as 1.20 kg/m^{3}, the cross-sectional area of the feather as 0.02 m^{2}, and the drag coefficient as 0.05.

**Solution**

Given data:

- Air resistance force acting on a feather, F
_{D}= ? - Velocity of a feather, v = 8 m/s
- Density of the air, ρ = 1.20 kg/m
^{3} - Cross sectional area of a feather, A = 0.02 m
^{2} - Drag coefficient, C
_{D}= 0.05

Applying the formula:

- F
_{D}= ½ × ρ A C_{D}v^{2} - F
_{D}= ½ × 1.20 × 0.02 × 0.05 × (8)^{2} - F
_{D}= 0.03 N

Therefore, the air resistance force acting on a feather is **0.03 N**.

### Problem #2

When a skydiver jumps from a plane, the skydiver falls with a velocity of 45 m/s. Determine the air resistance force acting on the skydiver, considering the density of the air as 1.25 kg/m^{3}, the cross-sectional area of the skydiver as 0.20 m^{2}, and the drag coefficient as 0.70.

**Solution**

Given data:

- Velocity of a skydiver, v = 45 m/s
- Air resistance force acting on a skydiver, F
_{D}= ? - Density of the air, ρ = 1.25 kg/m
^{3} - Cross sectional area of a skydiver, A = 0.20 m
^{2} - Drag coefficient, C
_{D}= 0.70

Applying the formula:

- F
_{D}= ½ × ρ A C_{D}v^{2} - F
_{D}= ½ × 1.25 × 0.20 × 0.70 × (45)^{2} - F
_{D}= 177.18 N

Therefore, the air resistance force acting on a skydiver is **177.18 N**.

### Problem #3

A leaf is descending from a certain height with a velocity of 10 m/s while floating in the air. Find the air resistance force acting on the leaf, taking into account the density of the air as 1.22 kg/m^{3}, the cross-sectional area of the leaf as 0.05 m^{2}, and the drag coefficient as 0.08.

**Solution**

Given data:

- Velocity of a leaf, v = 10 m/s
- Air resistance force acting on a leaf, F
_{D}= ? - Density of the air, ρ = 1.22 kg/m
^{3} - Cross sectional area of a leaf, A = 0.05 m
^{2} - Drag coefficient, C
_{D}= 0.08

Applying the formula:

- F
_{D}= ½ × ρ A C_{D}v^{2} - F
_{D}= ½ × 1.22 × 0.05 × 0.08 × (10)^{2} - F
_{D}= 0.24 N

Therefore, the air resistance force acting on a leaf is **0.13 N**.

### Problem #4

Find the value of the air resistance force acting on a parachute bag that is falling with a velocity of 30 m/s after being thrown from a helicopter. Given the density of the air as 1.21 kg/m^{3}, the cross-sectional area of the parachute bag as 0.10 m^{2}, and the drag coefficient as 0.12.

**Solution**

Given data:

- Air resistance force acting on a parachute bag, F
_{D}= ? - Velocity of a parachute bag, v = 30 m/s
- Density of the air, ρ = 1.21 kg/m
^{3} - Cross sectional area of a parachute bag, A = 0.10 m
^{2} - Drag coefficient, C
_{D}= 0.12

Applying the formula:

- F
_{D}= ½ × ρ A C_{D}v^{2} - F
_{D}= ½ × 1.21 × 0.10 × 0.12 × (30)^{2} - F
_{D}= 6.53 N

Therefore, the air resistance force acting on a parachute bag is **6.53 N**.

## Related

## More topics

- 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

- https://www.softschools.com/formulas/physics/air_resistance_formula/85/
- https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/falling.html
- https://lambdageeks.com/how-to-calculate-air-resistance/
- https://howthingsfly.si.edu/ask-an-explainer/how-do-you-calculate-force-air-resistance
- https://study.com/learn/lesson/free-fall-air-resistance-formula-force-examples.html
- https://www.omnicalculator.com/physics/free-fall-air-resistance
- https://www.studysmarter.us/explanations/physics/kinematics-physics/air-resistance/