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suchara

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## Homework Statement

Finding the velocity of a gliding object with an initial thrust-velocity of V after time t.

Constants are:-

g: gravity

a: constant for angle of attack, lift coefficient, air density and wing-area

## Homework Equations

[tex]L \propto a*V^2[/tex]

acceleration = v (dv/dt)

V is the airspeed of the object

## The Attempt at a Solution

I know lift is a force and has an acceleration. So thinking of Lift in terms of velocity-dependant acceleration and only focusing on Vy

acceleration = -g + a*v^2

[tex]v (dv/dt) = -g + a*v^2 [/tex]

[tex]dv/dt = -g/v + a*v [/tex]

[tex]dv/((-g/v) + a*v) = dt[/tex]

[tex]\int_{v_0}^v dv/(-g/v + a*v) = \int_{0}^t dt[/tex]

I havent done integration in a long time.. also Im confused about the notation

Heres the equation I get

[tex]\Big|_{v_0}^v (g*ln((a*v^2)-g) + a*v^2)/(a*v^2) = t [/tex]

After this.. Im unsure on how to proceed further

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