A ball is thrown from ground at an angle θ 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, ball rebounds at the same angle θ but with a reduced speed of u 0 α . Its motion continues for a long time as shown in figure. If the magnitude of avera

Step-by-step solution

For first projectile Average velocity, V = R T = U x = V 1 w h e r e R = R a n g e a n d T = T i m e o f f l i g h t R = 2 U x . U y g T = 2 . U y g For journey V 1 → n = R 1 + R 2 + … + R n T 1 + T 2 + … + T n = 2 u x 1 u y 1 g + 2 u x 2 u y 2 g + … + 2 u x n u y n g 2 u y 1 g + 2 u y 2 g + … 2 u y n g ⇒ U x 1 + 1 α 2 + 1 α 4 + … 1 α 2 n 1 + 1 α + 1 α 2 + … + 1 α n = 0.8 v 1 , 1 + 1 α 2 + 1 α 4 + … 1 α 2 n ⇒ G e o m e t r i c p r o g r e s s i o n S u m o f G . P . = 1 1 - α 2 ⇒ V 1 1 1 - 1 α 2 1 1 - 1 α = 0.8 v 1