A golf ball is dropped from a height of 81 inches. It rebounds to 2/3 of its original height and continues rebounding in this manner. How far does it travel before coming to rest?

Question

mathmale · Answer

Sounds like a problem involving geometric series.  I'd suggest you draw a diagram showing each drop and each rebound.

If this were just a simple geometric series, you'd write $$\sum_{n=1}^{infinity}a*r ^{n-1}, n: {1,2,3,...}$$  but there's more to the present problem than that.  What;'s extra?

anonymous · Answer

when the golf ball is first dropped it will cover 81 m 
 then it rebounds to cover 2/3 of 81 =54m 
 then it falls back 54m 
 then it rebounds 2/3 of 54 =36m 
 falls back 36m 
 so total distance = 81 +(54+54+36+36+.....+0 ) 
 81 +2(an G.P with first term = 54 comm diff = 2/3) 
 81 +2(162) (USING INFINITE G.P FORMULA ) 
 =405m 
i found this online but what do they mean by ( an G.P with first term)

mathmale · Answer

What do y ou mean by G. P.?  I think the G stands for Geometric; the P possibly for Progression.

anonymous · Answer

im not sure what It means but I think G is for geometric and p for series

rock_mit182 · Answer

GEOmetric progression

rock_mit182 · Answer

also known as geometric sequence

rock_mit182 · Answer

$$a _{n}=a _{n-1}*r$$
 for every integer n >= 1.

rock_mit182 · Answer

or also $$a _{n+1} = a _{n} *r$$

rock_mit182 · Answer

where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence's start value