Jawaban:

Pembahasan

Masalah tersebut dapat diselesaikan dengan konsep jumlah tak hingga deret geometri

Saat bola gerak ke atas/ memantul

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Panjang lintasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight S apostrophe subscript infinity end cell equals cell fraction numerator straight a over denominator 1 minus straight r end fraction end cell row blank equals cell fraction numerator 17 over denominator 1 minus begin display style 4 over 7 end style end fraction end cell row blank equals cell fraction numerator 17 over denominator begin display style 3 over 7 end style end fraction end cell row blank equals cell fraction numerator 17 cross times 7 over denominator 3 end fraction end cell row blank equals cell 39 comma 7 space straight m end cell end table end style

Saat bola jatuh/ gerak kebawa;

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a apostrophe end cell equals 17 row cell straight r apostrophe end cell equals cell 4 over 7 end cell end table end style

Panjang lintasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight S apostrophe subscript infinity end cell equals cell fraction numerator straight a apostrophe over denominator 1 minus straight r apostrophe end fraction end cell row blank equals cell fraction numerator 17 over denominator 1 minus begin display style 4 over 7 end style end fraction end cell row blank equals cell fraction numerator 17 over denominator begin display style 3 over 7 end style end fraction end cell row blank equals cell fraction numerator 17 cross times 7 over denominator 3 end fraction end cell row blank equals cell 39 comma 7 space straight m end cell end table end style

Jadi total panjang lintasan bola sampai berhenti adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell panjang space lintasan space end cell equals cell straight S apostrophe subscript infinity plus straight S apostrophe apostrophe subscript infinity end cell row blank equals cell 39 comma 7 plus 39 comma 7 end cell row blank equals cell 79 comma 4 space straight m end cell end table end style

Jadi panjang lintasan bola adalah begin mathsize 14px style 79 comma 4 space straight m end style.