Calculate the ratio of the drag force on a jet flying at 1049 km/h at an altitude of 10.0 km to the drag force on a prop-driven transport flying at 560 km/h and at an altitude of 5.00 km. The density of air is 0.380 kg/m3 at 10.0 km and 0.670 kg/m3 at 5.00 km. Assume that the airplanes have the same effective cross-sectional area and drag coefficient C.

Question

Calculate the ratio of the drag force on a jet flying at 1049 km/h at an altitude of 10.0 km to the drag force on a prop-driven transport flying at 560 km/h and at an altitude of 5.00 km. The density of air is 0.380 kg/m3 at 10.0 km and 0.670 kg/m3 at 5.00 km. Assume that the airplanes have the same effective cross-sectional area and drag coefficient C.

Answer 1

The drag force in each case is

C*(1/2)*(air density)*V^2

Ratio (jet/prop) = (0.380/0.670)*(1049/560)^2 = 1.99

Note that I did not have to change dimensions to m/s, since I used the same velocity dimensions for both planes.

Answer 2

Thank you so much... Huge help

Answer 3

It's very helpful and its explained in simple terms which makes it easier to understand.

Answer 4

To calculate the ratio of the drag force on the two planes, we need to use the drag force equation:

Drag Force = 0.5 * Drag Coefficient * Density * Velocity^2 * Area

Given:
- Jet flying at 1049 km/h at an altitude of 10.0 km
- Prop-driven transport flying at 560 km/h at an altitude of 5.00 km
- Density of air is 0.380 kg/m^3 at 10.0 km
- Density of air is 0.670 kg/m^3 at 5.00 km
- Assume the airplanes have the same effective cross-sectional area and drag coefficient C

Let's calculate the ratio step by step:

Step 1: Convert the velocities from km/h to m/s.

Jet velocity = 1049 km/h * (1000 m/km) / (3600 s/h) = 291.39 m/s
Transport velocity = 560 km/h * (1000 m/km) / (3600 s/h) = 155.56 m/s

Step 2: Calculate the ratio of the densities.

Density ratio = Density at 10.0 km / Density at 5.00 km
= 0.380 kg/m^3 / 0.670 kg/m^3
= 0.567 (rounded to three decimal places)

Step 3: Calculate the ratio of the drag forces.

Drag force ratio = (Drag Force on Jet / Drag Force on Transport)

Using the drag force equation, we can eliminate the area and drag coefficient since they are assumed to be the same for both planes.

Drag force ratio = (0.5 * Density at 10.0 km * Jet velocity^2) / (0.5 * Density at 5.00 km * Transport velocity^2)

Simplifying the equation:

Drag force ratio = (Density at 10.0 km / Density at 5.00 km) * (Jet velocity^2 / Transport velocity^2)
= 0.567 * (291.39 m/s)^2 / (155.56 m/s)^2

Calculating the values:

Drag force ratio ≈ 0.567 * 84863.8 m^2/s^2 / 24176.7 m^2/s^2
≈ 2.00

Therefore, the ratio of the drag force on the jet to the drag force on the prop-driven transport is approximately 2.00.