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A ball is thrown from ground at an angle...

A ball is thrown from ground at an angle `theta` with horizontal and with an initial speed `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, the ball rebounds at the same angle `theta` but with a reduced speed of `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 `V_1` ,. the value of `alpha` is ________.

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