A space b a l l space i s space d r o p p e d space f r o m space a space h e i g h t space o f space 100 m space a n d space i t space r e b o u n d s space t o space 1 half space o f space t h e space h e i g h t space i t space f a l l s.
I t space c o n t i n u e s space t o space f a l l space a n d space r e b o u n d. F i n d space t h e space t o t a l space d i s tan c e space t h e space b a l l space c a n space t r a v e l space b e f o r e space c o m i n g space t o space r e s t ? space

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Asked by Topperlearning User | 7th Oct, 2016, 04:17: PM

Expert Answer:

1 s t space t i m e space t h e space b a l l space t r a v e l s equals 100 m
A f t e r space h i t t i n g space t h e space g r o u n d space i t space r i s e s space t o space 50 m space a n d space f a l l s space b y space 50 m space s o space
2 n d space t i m e space t h e space b a l l space t r a v e l s equals 100 m equals 100 cross times 1 half cross times 2
3 r d space t i m e space t h e space b a l l space r i s e s space b y space 25 m space a n d space f a l l s space b y space 25 m space s o
t h e space d i s tan c e space t r a v e l l e d equals 50 m equals 100 cross times left parenthesis 1 half right parenthesis squared cross times 2
t h e space p r o c e s s space w i l l space c o n t i n u e space u n t i l space t h e space b a l l space c o m e s space t o space r e s t. S o space t h e space t o t a l space d i s tan c e space t r a v e l l e d
i s
100 plus 100 cross times 2 open parentheses 1 half plus 1 fourth plus 1 over 8 plus... close parentheses
100 plus 200 open parentheses fraction numerator begin display style 1 half end style over denominator 1 minus begin display style 1 half end style end fraction close parentheses equals 100 plus 200 equals 300 m

Answered by  | 7th Oct, 2016, 06:17: PM

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