Question

A ball is dropped from a height 64 m 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

The correct option is C $2^{-10}m$

Since height attained after every hit is $\frac{1}{2}$ of the previous one so the height attained after hitting the ground for the 16th time
$=64\times {\left(\frac{1}{2}\right)}^{16}=2^6\times 2^{-16}=2^{-10}$.