Finding the average magnitude of the drag force

[rickyjoepr]

Homework Statement

A saucer of mass 1.75x10^9 enters
1.the gravitational field of PlanetX and enters its atmosphere; the gravitational field of the planet is 10.6 m/s2 and is considered uniform throughout the 80-km thick atmosphere.
If the saucer enters the atmosphere at 460 m/s and slows down to 110 m/s before its crash-landing, what is the average magnitude of the drag force (gravity cannot be neglected)?
[/B]

Homework Equations

drag for disk, D = (1/4) AV^2
W = Total Mechanical Energy

The Attempt at a Solution

E1 = (1/2)m1Vi^2 + mgd
E2 = 0 + 0

So W = (1/2)m1V1+mgd

Because W = Fd

W/d = F

2.55 x10^10

However the correct answer is listed as 2.07 x 10^10 N

I am not sure if my method of using mechanical energy is correct., Or wether I should be using the drag force equation to solve the problem

 

[ehild]

Homework Statement

A saucer of mass 1.75x10^9 enters
1.the gravitational field of PlanetX and enters its atmosphere; the gravitational field of the planet is 10.6 m/s2 and is considered uniform throughout the 80-km thick atmosphere.
If the saucer enters the atmosphere at 460 m/s and slows down to 110 m/s before its crash-landing, what is the average magnitude of the drag force (gravity cannot be neglected)?
[/B]

Homework Equations

drag for disk, D = (1/4) AV^2
W = Total Mechanical Energy

The Attempt at a Solution

E1 = (1/2)m1Vi^2 + mgd
E2 = 0 + 0

So W = (1/2)m1V1+mgd

Because W = Fd

W/d = F

2.55 x10^10

However the correct answer is listed as 2.07 x 10^10 N

I am not sure if my method of using mechanical energy is correct., Or wether I should be using the drag force equation to solve the problem

The speed is not zero before the crash.

 

[haruspex]

W/d = F

The use of this to find an average force is not valid, though I realize it is what you are forced to use in this question.
Average force is defined as (change in momentum)/(elapsed time). If the force is not constant then (change in energy)/(distance) will not usually produce the same value.