# Average force of air resistance

[SOLVED] Average force of air resistance

In early test flights for the space shuttle using a "glider" (mass of 1500kg including pilot), it was noted that after a horizontal launch at 750km/h at a height of 4500m, the glider eventually landed at a speed of 300km/h. What would it's landing speed have been in the absence of air resistance? What was the average force of air resistance exerted on the shuttle if it came in at a constant angle of 10 degrees to the earth?

I converted vi to 208.33 m/s and vf to 83.33 m/s.

I think I answered the first part correctly using 1/2mvi^2 + mgyi = 1/2mvf^2 + mgyf. I calcualted vf = 362.77 m/s. I double checked this using kinematic equations and got the same answer.

I'm having problems with the second part. I believe air resistance is a nonconservative force. The only equation that I came up with is:

wnc = change in KE + change in PE

From this I derived:

Fyi cos 10 = 1/2mvf^2 - 1/2mvi^2 + mgyf - mgyi

Using this I came up with the answer -21097 N but this doesn't seem right. What am I missing here?

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I think I figured out where I went wrong.
d = yi/sin 10 making w = Fdcos 180 = -Fd = -F(yi/sin 10)

This would give me the following equation:

-F(yi/sin10) = (1/2mvf^2 - 1/2mvi^2) + (mgyf - mgyi)

Then solve for F. F = 3608N