A ball is thrown from ground at an angle θ with horizontal and with an initial speed u₀. 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 V₁. After hitting the ground, the ball rebounds at the same angle θ but with a reduced speed of u₀/α. 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 0.8V₁, the value of α is _____.