# Air Friction Stops my Projectile

From the origin of a Cartesian coordinate system, a particle of mass $m$ is thrown with an initial speed $v_{0}$ at an angle of $\theta=\frac{\pi}{3}$ from the horizontal x-axis. The air friction $f$ acts on the particle such that $\vec{f} = - b\vec{v},$ where $b$ is a positive constant and $\vec{v}$ is the velocity of the particle. If the x cordinate where the particle will only have vertical speed can be writen as $x=\dfrac{\alpha\cdot mv_{0}}{\beta \cdot b}.$ Find the value of $\alpha+\beta.$

The gravity acts in the vertically downward direction as $\vec{g}=-g\hat{y}$.

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