A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed $\mathrm{u}_0$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V_1$. After hitting the ground, ball rebounds at the same angle $\theta$ but with a reduced speed of $\mathrm{u}_0 / \alpha$. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8 \mathrm{~V}_1$, the value of $\alpha$ is $\_\_\_\_$