Question

A rubber ball is released from a height of $5\,m$ above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g =10\,ms ^{-2}$ )

• A. $3.0\,ms ^{-1}$
• B. $3.50\,ms ^{-1}$
• C. $2.0\,ms ^{-1}$
• D. $2.50\,ms ^{-1}$

Answer 1

Answer: (D)

$v _{0}=\sqrt{2 gh }$
$v = e \sqrt{2 gh }=\sqrt{2 gh }$
$\Rightarrow e =0.9$
$S = h +2 e ^{2} h +2 e ^{4} h +\ldots \ldots \ldots$
$t=\sqrt{\frac{2 h}{g}}+2 e \sqrt{\frac{2 h}{g}}+2 e^{2} \sqrt{\frac{2 h}{g}}+\ldots \ldots . .$
$v _{ av }=\frac{ S }{ t }=2.5\, m / s$