Question

In a lecture demonstration a small steel ball bounces on a steel plate. On each bounce the downward speed of the ball arriving at the plate is reduced by a factor e in the rebound. If the ball was initially dropped from a height of 50 cm above the plate at time t = 0, and if 30 seconds later the silencing of a microphone sound indicated all bouncing had ceased, what was the value of e?

Answer 1

it is easy for the question to find a solution. just have a bit try!

Answer 2

I have tried.. that why I posted it on here.

Answer 3

solve for t first
using constant acceleration motion equation with ur given values. all with same units. meter, second. convert cm to m.
\[h=X_{final}-X_{o}=V_{o}t+\frac{ 1 }{ 2 }At^{2}\]
U said: On each bounce the downward speed of the ball arriving at the plate is reduced by a factor e in the rebound.
1st impact has no e. 2nd has one e, 3rd is 2nd multiplied by e so on....
1st impact is not round trip. 2nd 3rd .... r all round trips that's why multiplied by 2.
time total = t + 2te + 2tee + 2teee +.....
->time total = (-t +t )+t + 2te + 2tee + 2teee +.....
->time total = -t +2t + 2te + 2tee + 2teee +.....
->time total = -t +2t(1 + e + ee +eee +.....)
taylor macurlin series(Cal 2) for this fraction
\[\frac{ 1 }{ (1-e) }=\sum_{n=0}^{\infty}e^{n}=1+e+e^{2}+e^{3}...\]
plug in the fraction above then solve for e