A ball falls from a height h and rebounds after striking the floor. The coefficient of restitution is e . The maximum distance covered before it comes to rest is

Step-by-step solution

Ball falls from height h then formula for height covered by it in n th rebound is given by h_n=h e^ 2 n where e= coefficient of restitution n= number of rebound Total distance travelled by particle before rebounding has stopped. H=h+2 h₁+2 h₂+2 h_n+ =h+2 h e^2+2 h e^4+2 h e^6+2 h e^8+ =h+2 h (e^2+e^4+e^6+e^8+ )=h+2 h [ e^2 1-e^2 ]=h [1+ 2 e^2 1-e^2 ]=h [ 1+e^2 1-e^2 ]