<![CDATA[An interesting problem (3)]]>A solid rubber ball rebounds to three-fourths the height it is dropped from. What is the total vertical distance traveled by a ball dropped from a height of 24 feet as it bounces to rest?
]]>https://forum.poshenloh.com/topic/999/an-interesting-problem-3RSS for NodeTue, 21 Mar 2023 01:34:50 GMTSat, 12 Feb 2022 04:56:46 GMT60<![CDATA[Reply to An interesting problem (3) on Sat, 05 Mar 2022 17:52:33 GMT]]>24+3/4(24)(2)+(3/4^2)(24)(2)+(3/4^3)(24)(2)+.....
(The x2 is because the ball drops the same distance up and down)

This is an infinite arithmetic sequence.

Let S = 3/4(24)(2)+(3/4^2)(24)(2)+... = 36+(3/4)(36)+(3/4^2)(36)+....
So 4/3S=48+36+(3/4)(36)+....
So 4/3S-S=1/3S=48
So S=144
So S+24=168?

]]>https://forum.poshenloh.com/post/5239https://forum.poshenloh.com/post/5239Sat, 05 Mar 2022 17:52:33 GMT