{"id":6551,"date":"2011-03-01T15:47:23","date_gmt":"2011-03-01T15:47:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6551"},"modified":"2022-01-14T18:12:19","modified_gmt":"2022-01-14T18:12:19","slug":"um-projectil-e-lancado-do-solo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6551","title":{"rendered":"Um proj\u00e9til \u00e9 lan\u00e7ado do solo"},"content":{"rendered":"<p><ul id='GTTabs_ul_6551' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6551' class='GTTabs_curr'><a  id=\"6551_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6551' ><a  id=\"6551_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6551'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um proj\u00e9til \u00e9 lan\u00e7ado do solo, verticalmente, com uma velocidade inicial de 115 m\/s. Ap\u00f3s $t$ segundos a sua dist\u00e2ncia $d$ ao solo \u00e9 dada por:<br \/>\n\\[d(t)=115t-5{{t}^{2}}\\]<\/p>\n<ol>\n<li>Determine o valor da velocidade nos instantes $t=2$ e $t=3$.<\/li>\n<li>Quando \u00e9 que o proj\u00e9til atinge o solo?<br \/>\nDetermine o valor da sua velocidade nesse instante.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6551' onClick='GTTabs_show(1,6551)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6551'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>A velocidade do proj\u00e9til \u00e9 dada por $d&#8217;(t)=115-10t$.<br \/>\nPortanto, $d&#8217;(2)=115-10\\times 2=95\\,m\/s$ e $d&#8217;(3)=115-10\\times 3=85\\,m\/s$.<br \/>\n\u00ad<\/li>\n<li>Ora, $d(t)=0\\Leftrightarrow 115t-5{{t}^{2}}=0\\Leftrightarrow 5t(23-t)=0\\Leftrightarrow t=0\\vee t=23$.<br \/>\nO proj\u00e9til atinge o solo 23 segundos ap\u00f3s o seu lan\u00e7amento.<\/p>\n<p>Nesse instante, a sua velocidade \u00e9 $d&#8217;(23)=115-10\\times 23=-115\\,m\/s$.<\/p>\n<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":726,\r\n\"height\":480,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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Ap\u00f3s $t$ segundos a sua dist\u00e2ncia $d$ ao solo \u00e9 dada por: \\[d(t)=115t-5{{t}^{2}}\\] Determine o valor da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19444,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[136],"series":[],"class_list":["post-6551","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivada"],"views":1898,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/Projetil_lancado_verticalmente.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6551"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6551\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19444"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6551"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}