Question

A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plate is reduced by a factor e (coefficient of restitution) in the rebound, so that
$$
\mathrm{V}_{\text {upward }}=\mathrm{eV}_{\text {downward }}
$$
If the ball is initially dropped from a height of \(0.4 \mathrm{~m}\) above the plate and if 10 seconds later the bouncing ceases, he value of \(e\) is
(A) \(\sqrt{\frac{2}{7}}\)
(B) \(\frac{3}{4}\)
(C) \(\frac{13}{18}\)
(D) \(\frac{17}{18}\)

Answer 1

Ans:(D)
$$
h_{n}=e^{2 n} \cdot h
$$
$$
\begin{aligned}
\therefore t &=\sqrt{\frac{2 h}{g}}+2 \sqrt{\frac{2 h e^{2}}{g}}+2 \sqrt{\frac{2 h e^{4}}{g}}+\ldots . .=\sqrt{\frac{2 h}{g}}\left[1+2 e+2 e^{2}+\ldots\right] \\
&=\sqrt{\frac{2 h}{g}\left[\frac{1+e}{1-e}\right] \quad \therefore 10}=\sqrt{\frac{2(0.4)}{10}\left(\frac{1+e}{1-e}\right)} \therefore e=\frac{25 \sqrt{2}-1}{25 \sqrt{2}+1} \approx \frac{17}{18}
\end{aligned}
$$

Answer 2

buy cialis 40mg for sale <a href="https://ordergnonline.com/">tadalafil over counter</a> causes of ed