Drag force or **Air resistance force** (F_{D}) is equal to half times the product of **density **(ρ), **cross sectional area** (A), **drag coefficient** (C_{D}) and the square of **velocity **(v). Using the formula of air resistance: **F**_{D}** = ½ × ρ A C**_{D}** v**** ^{2}**, the value of air resistance force acting on a falling object can be calculated.

Let’s solve some problems based on this formula, so you’ll get a clear idea.

## Air Resistance Practice Problems

**Problem 1:** Calculate the air resistance force acting on a feather falling with a velocity of 8 m/s. If the density of the air is 1.20 kg/m^{3}, the cross sectional area of a feather is 0.02 m^{2}, and the drag coefficient is 0.05.

Solution:

Given data:

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

Air resistance force acting on a feather, F_{D} = ?

Using the formula of air resistance,

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, a skydiver is falling with the velocity of 45 m/s. Calculate the air resistance force acting on a skydiver, if the density of the air is 1.25 kg/m^{3}, the cross sectional area of a skydiver is 0.20 m^{2}, and the drag coefficient is 0.70.

Solution:

Given data:

Velocity of a skydiver, v = 45 m/s

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

Air resistance force acting on a skydiver, F_{D} = ?

Using the formula of air resistance,

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:** One leaf (floating in the air) is falling down from some height with the velocity of 10 m/s. If the density of the air is 1.22 kg/m^{3}, the cross sectional area of a leaf is 0.05 m^{2}, and the drag coefficient is 0.08, then find the value of the air resistance force acting on a leaf.

Solution:

Given data:

Velocity of a leaf, v = 10 m/s

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

Air resistance force acting on a leaf, F_{D} = ?

Using the formula of air resistance,

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:** What is the value of the air resistance force acting on a parachute bag falling with the velocity of 30 m/s, when it is thrown from a helicopter? The density of the air is 1.21 kg/m^{3}, the cross sectional area of a parachute bag is 0.10 m^{2}, and the drag coefficient is 0.12.

Solution:

Given data:

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

Air resistance force acting on a parachute bag, F_{D} = ?

Using the formula of air resistance,

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**.

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**Related:**

- Free Fall Equation
- Terminal Velocity Equation
- Gravity Equation
- Inertia Formula
- Acceleration Formula
- Momentum Equation
- Mass Formula
- Velocity Formula
- Pressure Equation
- Kinematic Equations
- Friction Equation

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