{"id":6351,"date":"2024-05-26T11:35:00","date_gmt":"2024-05-26T14:35:00","guid":{"rendered":"https:\/\/xequematenem.com.br\/blog\/?p=6351"},"modified":"2025-06-10T18:34:46","modified_gmt":"2025-06-10T21:34:46","slug":"questao-164-enem-ppl-2020-4","status":"publish","type":"post","link":"https:\/\/xequematenem.com.br\/blog\/questao-164-enem-ppl-2020-4\/","title":{"rendered":"Quest\u00e3o 164 &#8211; Enem PPL 2020"},"content":{"rendered":"\n<p class=\"has-text-align-left wp-block-paragraph\">Dois atletas partem de pontos, respectivamente P<sub>1<\/sub> e P<sub>2<\/sub> , em duas pistas planas distintas, conforme a figura, deslocando-se no sentido <strong>anti-hor\u00e1rio at\u00e9 a linha de chegada, percorrendo, desta forma, a mesma dist\u00e2ncia (L)<\/strong>. Os trechos retos dos finais das curvas at\u00e9 a li<strong>nha de chegada desse percurso t\u00eam o mesmo comprimento (l)<\/strong> nas duas pistas e s\u00e3o tangentes aos trechos curvos, que s\u00e3o semic\u00edrculos de centro C. <strong>O raio do semic\u00edrculo maior \u00e9 R<sub>1<\/sub> e o raio do semic\u00edrculo menor \u00e9 R<sub>2<\/sub> .<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"315\" height=\"166\" src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-75.png\" alt=\"\" class=\"wp-image-6353\" title=\"\" srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-75.png 315w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-75-300x158.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sabe-se que o comprimento de um arco circular \u00e9 dado pelo produto do seu raio pelo \u00e2ngulo, medido em radiano, subentendido pelo arco.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Nas condi\u00e7\u00f5es apresentadas, a raz\u00e3o da medida do \u00e2ngulo P<\/strong><strong><sub>2<\/sub><\/strong><strong>CP<\/strong><strong><sub>1<\/sub><\/strong><strong> pela diferen\u00e7a L\u2212 l \u00e9 dada por&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"89\" height=\"253\" data-src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-74.png\" alt=\"\" class=\"wp-image-6352 lazyload\" title=\"\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 89px; --smush-placeholder-aspect-ratio: 89\/253;\"><\/figure>\n\n\n\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Queremos saber a raz\u00e3o entre o \u00e2ngulo P<sub>2<\/sub>CP<sub>1<\/sub> (<strong>\u03b8<\/strong>) e a diferen\u00e7a L\u2212 l ,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u03b8 \/ (L &#8211; I)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Precisamos calcular a rela\u00e7\u00e3o entre o comprimento dos arcos e os \u00e2ngulos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sabemos que o arco S1 corresponde ao \u00e2ngulo \u03b1.\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"561\" height=\"294\" data-src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/Dois-atletas-partem-de-pontos.png\" alt=\"\" class=\"wp-image-22736 lazyload\" title=\"\" data-srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/Dois-atletas-partem-de-pontos.png 561w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/Dois-atletas-partem-de-pontos-300x157.png 300w\" data-sizes=\"(max-width: 561px) 100vw, 561px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 561px; --smush-placeholder-aspect-ratio: 561\/294;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Como os atletas percorrem a mesma dist\u00e2ncia L, temos que:\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L = I + S<sub>1<\/sub>\u00a0 \u00a0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L =\u00a0 I + S<sub>2<\/sub>,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">logo:\u00a0<strong>S<sub>1<\/sub>\u00a0= S<sub>2<\/sub><\/strong>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sendo<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>S<sub>1<\/sub>\u00a0=<\/strong> \u03b1 . R<sub>1<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>S<sub>2<\/sub><\/strong> = (\u03b1 + \u03b8) . R<sub>2<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos ent\u00e3o concluir que:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1 . R<sub>1<\/sub>\u00a0 =\u00a0(\u03b1 + \u03b8) . R<sub>2<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1 . R<sub>1<\/sub>\u00a0 = \u03b1 . R<sub>2<\/sub>\u00a0+ \u03b8 . R<sub>2<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1 . R<sub>1<\/sub>\u00a0 &#8211; \u03b1 . R<sub>2<\/sub>\u00a0= \u03b8 . R<sub>2<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u03b8 =\u00a0<u>\u03b1 . R<sub>1<\/sub>\u00a0 &#8211; \u03b1 . R<sub>2<\/sub><\/u><br>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 R<sub>2<\/sub><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sendo L &#8211; I = S<sub>1<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos dizer que <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>L &#8211; I = S<sub>1<\/sub><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entao dividindo <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b8\u00a0\/\u00a0S<sub>1<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">teremos<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u03b8\/<\/strong>S<sub>1<\/sub><strong> =\u00a0<u>\u03b1 . R<sub>1<\/sub>\u00a0 &#8211; \u03b1 . R<sub>2<\/sub><\/u> = <\/strong>\u03b1 . R<sub>1<\/sub>\/R<sub>2<\/sub> .(\u03b1 . R1) &#8211; \u03b1 . R<sub>2<\/sub>\/R<sub>2<\/sub> .(\u03b1 . R1)<strong><br>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 R<sub>2<\/sub><\/strong> .(\u03b1 . R1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Simplificando as fra\u00e7\u00f5es:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u03b8\/<\/strong>S<sub>1<\/sub><strong> =<\/strong> 1\/R<sub>2<\/sub> &#8211; 1\/R<sub>1<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Alternativa C<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dois atletas partem de pontos, respectivamente P1 e P2 , em duas pistas planas distintas, conforme a figura, deslocando-se no sentido anti-hor\u00e1rio at\u00e9 a linha de chegada, percorrendo, desta forma, a mesma dist\u00e2ncia (L). Os trechos retos dos finais das curvas at\u00e9 a linha de chegada desse percurso t\u00eam o mesmo comprimento (l) nas duas [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":6353,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[87,99],"tags":[],"area-do-conhecimento":[132,118],"assunto":[50],"class_list":["post-6351","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-questoes-ppl","category-2020-questoes-ppl","area-do-conhecimento-matematica","area-do-conhecimento-matematica-e-suas-tecnologias","assunto-geometria-plana"],"_links":{"self":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/comments?post=6351"}],"version-history":[{"count":3,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6351\/revisions"}],"predecessor-version":[{"id":22737,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6351\/revisions\/22737"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media\/6353"}],"wp:attachment":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media?parent=6351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/categories?post=6351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/tags?post=6351"},{"taxonomy":"area-do-conhecimento","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/area-do-conhecimento?post=6351"},{"taxonomy":"assunto","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/assunto?post=6351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}