A ball is thrown from ground at an angle $$\theta$$ with horizontal and with aninitial speed $$\mu_0$$. 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, the ball rebounds at the same angle $$\theta$$ but with a reduced speed of $$\frac{\mu_0}{\alpha}$$. 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 $$0.8 V_1,$$ the value of $$\alpha$$ is __________ .