Question

An object is dropped from a height h from the ground. Every time it his the ground it looses $50\%$ of its kinetic energy. The total distance covered as t$\to \infty$ is:

• A. $2h$
• B. $\infty$
• C. $\frac{5}{3}h$
• D. $\frac{8}{3}h$

Answer 1

Answer: (B)

$\infty$

$h_i=$ height after $i^{th}$ collision

$h_2=\frac{{v_2}^2}{2g}=\frac{v^2}{2.2g}=\frac{h}{2}$

similarly$,$

$h_3=\frac{h}{4};$ $h_4=\frac{h}{8}$

total distance ravelled

$=h+\frac{h}{2}+\frac{h}{4}+\frac{h}{8}+---+\infty$

sum of infinite