what is the maximum height for a ball after n collisions if it loses 3/4 of its energy after each collision when dropped from a height h to a floor
At first, ball is at height h and energy=mgh
After each collision 3/4 energy is lost. Which means 1/4 th of previous value is remaining after each collision,
After the first collision energy, E1 = mg (h/4) and ball rises to h/4
Next collision the energy before the collision is E1 and after = E2= 1/4 E1
E2= 1/4[1/4 mgh] = (1/4)² m g h
After nth collision En= (1/4)n m g h
and height = (h/4)n