Question

a body of mass m falls from a height h to ground if coefficient of restitution is e then calculate the distance travelled by body before it comes to rest

Answer 1

to solve this let's find the relation between the height raised of the ball when it falls from a height 'h'.

let 'v' be the velocity of the ball when it hits the ground.

a = g

so v = at (let 't' be the time taken to hit the ground)
=> t = v/a
 
=> h = 0 x t + (1/2) a t^2   (t^2 -> t square)
 
so h = (v x v) / 2a

then it rebonds with 'ev' velocity.

so the height it reaches is h' = (ev) t1 - (1/2) a t1^2     (t1^2 -> t1 square)

t1 = ev/a     (v = u-at   and v = 0 and u = ev here)

so by substituting t1 in h' we get
h' = (e square) x(v square) / 2a  = (e square) x  h

so distance travelled = h + (e^2) h + (e^4) h + (e^6) h + .........  which is in gp

so total distance = (h  /  (1-(e square)))