Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Determine the horsepower required to overcome the wind drag on a streamlined car traveling 90 km/h if the drag coefficient C D is 0.2. The drag force is given by F D = ½ ρ V 2 AC D , where A is the projected area of the car and V is the velocity. The density ρ of air is 1.23 kg/m 3 . Use A = 2.3 m 2 .
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Identify the formula for drag force:
$$ F_D = \frac{1}{2} \rho V^2 A C_D $$
Step 2: Substitute the values into the formula:
- ρ (density of air) = 1.23 kg/m³
- V (velocity) = 90 km/h = 90 * \frac{1000}{3600} = 25 m/s
- A (projected area) = 2.3 m²
- C_D (drag coefficient) = 0.2
Therefore,
$$ F_D = \frac{1}{2} \times 1.23 \times (25)^2 \times 2.3 \times 0.2 $$
Step 3: Calculate the drag force:
$$ F_D = \frac{1}{2} \times 1.23 \times 625 \times 2.3 \times 0.2 $$
$$ F_D = 0.615 \times 625 \times 2.3 \times 0.2 $$
$$ F_D = 0.615 \times 625 \times 0.46 $$
$$ F_D = 0.615 \times 287.5 $$
$$ F_D \approx 176.56 N $$
Step 4: Calculate the power required to overcome the drag force: Power (P) is given by:
$$ P = F_D \times V $$
so,
$$ P = 176.56 N \times 25 m/s = 4414 W $$
Step 5: Convert watts to horsepower:
1 horsepower = 745.7 W
Therefore:
$$ P_{hp} = \frac{4414}{745.7} \approx 5.93 HP $$
Therefore, the horsepower required to overcome the wind drag on the car is approximately 5.93 HP.
$$ F_D = \frac{1}{2} \rho V^2 A C_D $$
Step 2: Substitute the values into the formula:
- ρ (density of air) = 1.23 kg/m³
- V (velocity) = 90 km/h = 90 * \frac{1000}{3600} = 25 m/s
- A (projected area) = 2.3 m²
- C_D (drag coefficient) = 0.2
Therefore,
$$ F_D = \frac{1}{2} \times 1.23 \times (25)^2 \times 2.3 \times 0.2 $$
Step 3: Calculate the drag force:
$$ F_D = \frac{1}{2} \times 1.23 \times 625 \times 2.3 \times 0.2 $$
$$ F_D = 0.615 \times 625 \times 2.3 \times 0.2 $$
$$ F_D = 0.615 \times 625 \times 0.46 $$
$$ F_D = 0.615 \times 287.5 $$
$$ F_D \approx 176.56 N $$
Step 4: Calculate the power required to overcome the drag force: Power (P) is given by:
$$ P = F_D \times V $$
so,
$$ P = 176.56 N \times 25 m/s = 4414 W $$
Step 5: Convert watts to horsepower:
1 horsepower = 745.7 W
Therefore:
$$ P_{hp} = \frac{4414}{745.7} \approx 5.93 HP $$
Therefore, the horsepower required to overcome the wind drag on the car is approximately 5.93 HP.
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