(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

acceleration = v (dv/dt)

V is the airspeed of the object

3. 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Kinematics of a gliding object

**Physics Forums | Science Articles, Homework Help, Discussion**