Calculate the ratio of the drag force on a passenger jet flying with a speed of 750 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at one-fifth the speed and half the altitude of the jet. At 10 km the density of air is 0.38 kg/m3 and at 5.0 km it is 0.67 kg/m3. Assume that the airplanes have the same effective cross-sectional area and the same drag coefficient C.
(drag on jet / drag on transport.
Please help :)
You must have been given some equations for drag force, these equations vary, but typically they depend on Area, a coefficeint, and velocity^2.
Post your equations and work, and I will critique.
Sorry, the equation given is:
D=1/2(Dp)(Area)(Velocity^2)
I do not understand what area I am trying to calculate and what the constant equals. How do I find Dp and Area???
To find the ratio of drag forces on the jet and the prop-driven transport, you can use the drag force equation:
D = (1/2) * Dp * A * V^2
where D is the drag force, Dp is the density of air, A is the cross-sectional area of the airplane, and V is the velocity of the airplane.
In this case, you are given the equations, so let's assume that the cross-sectional area A and the drag coefficient C are the same for both the jet and the prop-driven transport. Therefore, they cancel out when comparing the two drag forces. Now, let's focus on finding Dp for both the jet and the transport.
At an altitude of 10 km, the density of air Dp1 is given as 0.38 kg/m^3. At an altitude of 5.0 km, the density of air Dp2 is given as 0.67 kg/m^3.
To find the ratio of drag forces, we need to calculate the Dp values for both the jet and the transport. We can use the density of air values at the respective altitudes and the given equation.
For the jet:
Dp1 = 0.38 kg/m^3 (given)
V1 = 750 km/h = 750000 m/3600 s = 208.33 m/s (converted)
Area = ???? (unknown)
For the transport:
Dp2 = 0.67 kg/m^3 (given)
V2 = (1/5) * V1 = 41.67 m/s (given, one-fifth the speed of the jet)
Area = ???? (unknown)
To find the area, we need more information. The question states that the airplanes have the same effective cross-sectional area, but this value is not given. Without this information, we cannot calculate the exact ratio of drag forces.
Please check if you have any additional details about the cross-sectional area or any other relevant information that can help us solve the problem.