Question

A ball is dropped from a height of $900$ centimetres. Each time it rebounds, it rises to two-third of the height it has fallen through. The total distance travelled by the ball before it comes to rest in metres, is

• A. $27$
• B. $36$
• C. $18$
• D. $45$

Answer 1

The correct option is D $45$

$H=9$ metres
Total distance travelled by ball before it comes to rest is
$H+2[\frac{2}{3}H+{\left(\frac{2}{3}\right)}^{2}H+{\left(\frac{2}{3}\right)}^{3}H+\cdots \text{upto}\infty ]$
$=H+2H[\frac{2}{3}+{\left(\frac{2}{3}\right)}^2+{\left(\frac{2}{3}\right)}^3+\cdots \text{upto}\infty ]$
$=H+2H\left(\frac{\frac{2}{3}}{1-\frac{2}{3}}\right)$
$=H+4H=5H$
$=5\times 9=45$ metres