Drag Force Ratio: Jet vs Transport at 1200 km/h, 15 km Altitude

[Arman777]

Homework Statement

Calculate the ratio of the drag force on a jet flying at $1200 km/h$ at an atttude of $15 km$ to the drag force on a prop-driven transport flying at half that speed and altitude.The density of air is $0.38(\frac {kg} {m^3})$ at $10 km$ and $0.67(\frac {kg} {m^3})$ at $5 km$.Assume that the air-planes have the same effective cross-sectonal area and drag coefficient C

Homework Equations

$F_D=\frac 1 2CAρv^2$

The Attempt at a Solution

Here C and A are the same so $F_D$ jet will be $F_1$ and $F_D$ plane will be $F_2$
$F_1=ρ_1(v_1)^2$ and $F_2=ρ_2(v_2)^2$

The question ask ratio so we don't care about units ( I guess )

$ρ_1$ which at 15 km is I found approximately $0.235 (\frac {kg} {m^3})$ ( from Inverse ratio )
$ρ_2$ which at 7.5 km is I found $0.525 (\frac {kg} {m^3})$

So $\frac {F_1} {F_2}=4 \frac {0.235} {0.525}=1.79$

answer is 3.3

I don't know where I went wrong

Thank you

 

[mfb]

I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.

 

[Arman777]

I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.

Yeah...I don't know too.This is all writes in the question.

Thanks

 

[haruspex]

You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

 

[Arman777]

You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

I know...So I think I just let it go :)

 

[mfb]

You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

It wouldn't fit to those values either, but of they might have altered even more values.

 

[Arman777]

It wouldn't fit to those values either, but of they might have altered even more values.

What an interesting question...