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Heldensheld

Member

Registered: 2006-07-01

Posts: 25

One quick question...help thanks!

SEQUENCE AND SERIES

Geometric series

A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues unil the ball comes to rest.

a) Show that the total time of motion is given by 1 + 2(0.9) + 2(0.0)^2 + 2(0.9)^3 + .....

b) Find Sn for the series in a.

c) How long does it take for the ball to come to rest.

Please show how you came to the conclusions....ty.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: One quick question...help thanks!

Sn-0.9Sn= 1+ 2(0.9) -0.9 + 2(0.9)^2-2(0.9)^2 +...+2(0.9)^(n-1) -2(0.9)^(n-1)-2(0.9)^n
=1+0.9+0+...-2(0.9)^n

So Sn=10(1.9-2(0.9)^n)

n->smaller and smaller
Sn shall be no larger than 10(1.9)=19 as far as I am concerned.

The standard answer  to this  problem might be 19, meaning 2(0.9)^n has come to 0 as n has reached infinity.

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X'(y-Xβ)=0

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: One quick question...help thanks!

a) The first fall takes 1 second, the time rising and falling will be the same hence 2(0.9) for the next rise and fall. Each time around is 90% of the previous, so the next time is 90% of 90%, the next is 90% of 90% of 90%, etc, hence:

1 + 2(0.9) + 2(0.9)^2 + 2(0.9)^3 + ...

George has the rest of the answer

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Heldensheld

Member

Registered: 2006-07-01

Posts: 25

Re: One quick question...help thanks!

Thanks guys...I'll look at it when I'm back from camp.