(a) A particle is thrown from a height h horizontally towards a vertical wall with a speed v as shown in the figure. If the particle returns to the point of projection after suffering two elastic collisions, one with the wall and another with the ground, find the total time of flight. [Elastic collision means the velocity component perpendicular to the surface gets reversed during collision.]

(b) Touching a hemispherical dome of radius R there is a vertical tower of height `H = 4 R`. A boy projects a ball horizontally at speed u from the top of the tower. The ball strikes the dome at a height `(R)/(2)` from ground and rebounds. After rebounding the ball retraces back its path into the hands of the body. Find u.