A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?
Let h = height of ceiling.
ā speed before first impact = ā2gh ā speed after first impact = eā2gh
The ball comes back for second impact, now its speed just before second impact = speed after first impact.
ā before second impact, speed = eā2gh ā after second impact, speed = e2ā2gh
This speed is the initial speed u for upward motion after second impact.
High attained = u22g ā h2 = [e2ā2gh]22gāh2 = e2(2gh)2gāe = 1ā2