A vehicle travelling at 120 km/hr on a paved surface with an air density of 2.123 Kg/m³ has coefficient of drag of 0.50 and frontal area of 3.0 m². Calculate the air resistance and

The formula for air resistance (drag force) is:

$$F_D = \frac{1}{2} \rho v^2 C_D A$$

Where:

• $F_D$ is the air resistance (drag force)
• $\rho$ is the air density
• $v$ is the velocity of the vehicle
• $C_D$ is the coefficient of drag
• $A$ is the frontal area

Given values:

• Velocity ($v$) = $120\, \text{km/hr}$
• Air density ($\rho$) = $2.123\, \text{kg/m}^3$
• Coefficient of drag ($C_D$) = 0.50
• Frontal area ($A$) = $3.0\, \text{m}^2$

$$v = 120\, \text{km/hr} \times \frac{1000\, \text{m}}{1\, \text{km}} \times \frac{1\, \text{hr}}{3600\, \text{s}}$$ $$v = \frac{120 \times 1000}{3600}\, \text{m/s}$$ $$v = \frac{120000}{3600}\, \text{m/s}$$ $$v = \frac{100}{3}\, \text{m/s} \approx 33.333\, \text{m/s}$$

$$F_D = \frac{1}{2} \times 2.123 \times \left(\frac{10000}{9}\right) \times 0.50 \times 3.0$$ $$F_D = 0.5 \times 2.123 \times 1111.111... \times 0.5 \times 3.0$$ $$F_D = 1769.166...\, \text{N}$$

The air resistance is approximately $\text{1769.17 N}$.