Ball is projected at angle  $\alpha$ between two vertical walls such that in the absence of the wall its range would have been 5.01d. Given that all the collisions with walls are perfectly elastic.
Find total number of collisions with walls before the ball comes back to the ground?

Colliding with the wall its vertical component $\left(v_y\right)$ of velocity will remain unchanged. (component along common tangent direction remains unchanged) while horizontal component $\left(v_x\right)$ is reversed remaining same in magnitude. Thus, path of the particle will be as shown in figure.
b) total number of collisions with the walls before the ball comes back to the ground are nine.