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 travelled by the ball up to the 10th impact?
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 travelled by the ball up to the 10th impact?
- [KVPY 2010]
- A
$2 h\left(\frac{1-r^{10}}{1-r}\right)$
- B
$h\left(\frac{1-r^{20}}{1-r^2}\right)$
- C
$2 h\left(\frac{1-r^{20}}{1-r^3}\right)-h$
- D
$2 h\left(\frac{1-r^{20}}{1-r^2}\right)-h$
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