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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 haven't done integration in a long time.. also I am 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.. I am unsure on how to proceed further
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