BdMO National Secondary 2007#5

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samiul_samin
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Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Secondary 2007#5

Unread post by samiul_samin » Sat Feb 23, 2019 11:08 am

A ball is thrown upward vertically to a height of $650$ meters from ground.Each $2$ times it hits the ground it bounces $\dfrac 25$ of the height it fell in the previous stage.How much the ball will travel before it stops?

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Secondary 2007#5

Unread post by samiul_samin » Sat Feb 23, 2019 11:20 am

Hint
Use Geometric progression
Solution
For $20$ times $distance_{20}=650\times\dfrac {1-{(\dfrac 25)}^{20}}{1-\dfrac 25}$

For $n$ times $distance_{n}=650\times\dfrac {1-{(\dfrac 25)}^{n}}{1-\dfrac 25}$
We need to prove this easy formula :) :) :) .

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