KVPY2010PhysicsMotion in One Dimension
A ball is dropped vertically from a height of h onto a hard surface. If the ball rebounds from the surface with a fraction r of the speed with which it strikes the latter on each impact, what is the net distance traveled by the ball up to the 10^ th impact ?
Options
- A2 ~h 1- r ¹⁰ 1- r
- Bh 1- r ²⁰ 1- r ²
- C2 ~h 1- r ²² 1- r ² - h
- D2 ~h 1- r ²⁰ 1- r ² - h
Correct answer
D. 2 ~h 1- r ²⁰ 1- r ² - h
Step-by-step solution
Total distance = ( v ₀² g + r ² v ₀² ~g + r ⁴ v ₀² ~g + . upto 10^ th terms )- h = v ₀² ~g (1+ r ²+ r ⁴+ .+10^ th . term )- h also v₀= 2 g h array l Total distance =2 ~h ( 1- ( r ² )¹⁰ 1- r ² )- h or total distance = 2 ~h (1- r ²⁰ ) (1- r ² ) - h array