Question

A ball is dropped from a height $64m$ above the ground and every time it hits the ground it rises to a height equal to half of the previous. What is the height attained after it hits the ground for the 16th time?

• A. $2^{-12}m$
• B. $2^{-11}m$
• C. $2^{-10}m$
• D. $2^{-9}m$

Answer 1

Answer: (D)

$2^{-9}m$

Let the ball is droped from ht - 'h'

$\Rightarrow$ After striping with ground

height is $\frac{h}{2},$ then $\frac{h}{4}$ & soon

$\Rightarrow h,\frac{h}{2},\frac{h}{4},...$

This is a G.P. with $r=\frac{1}{2}$

$\therefore a_{16}=a{r}^{n-1}=\frac{h}{2^{15}}=\frac{64}{215}$

$\Rightarrow a_{16}=2^{-9}m$