Question

A ball is dropped from height h coefficient of restitution e forthecollision with ground is 1/2 to the power 1/8 no of rebpunds after which height becomes 1/4 of max height issn

Answer 1

Answer:

after 8 rebound height becomes 1/4 of max height

Step-by-step explanation:

A ball is dropped from height h coefficient of restitution e for the collision with ground is 1/2 to the power 1/8 no of rebounds after which height becomes 1/4 of max height

coefficient of restitution = e = $(\frac{1}{2} )^{\frac{1}{8}$

Height after one rebound = Originial Height * e²

Let say after n rebound height become 1/4 of max height (original height)

Height after n rebound = Originial Height * e²ⁿ

Height after n rebound  = Originial height /4

Originial Height * e²ⁿ = Originial height /4

=> e²ⁿ = 1/4

=> $(\frac{1}{2})^{\frac{2n}{8}} = \frac{1}{4} \\\implies (\frac{1}{2})^{\frac{n}{4}} = (\frac{1}{2})^2 \\\\\implies \frac{n}{4} = 2\\ \\\implies n = 8$

after 8 rebound height becomes 1/4 of max height