{"id":1385,"date":"2024-05-10T21:51:58","date_gmt":"2024-05-10T21:51:58","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1385"},"modified":"2025-08-13T15:49:44","modified_gmt":"2025-08-13T15:49:44","slug":"applications-and-inequalities-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/applications-and-inequalities-apply-it-1\/","title":{"raw":"Applications of Non-Linear Equations: Apply It 1","rendered":"Applications of Non-Linear Equations: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Build and use equations and formulas that aren't straight lines to solve real-life problems.<\/li>\r\n<\/ul>\r\n<\/section>In 2014, Margit Tall made history in Helsinki, Finland. At age [latex]95[\/latex], she became one of the oldest bungee jumpers in the world, taking a thrilling plunge from a crane [latex]150[\/latex] meters above the sea.\r\n\r\n[caption id=\"attachment_6772\" align=\"aligncenter\" width=\"300\"]<img class=\"wp-image-6772 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-300x200.jpg\" alt=\"\" width=\"300\" height=\"200\" \/> Photo of bungee jumping; Photo by Carlos Ruiz on Pexels[\/caption]\r\n<p class=\"whitespace-pre-wrap break-words\">Before attempting a bungee jump, it's crucial to understand the physics behind the experience. Each jump consists of two main phases:<\/p>\r\n\r\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">The freefall phase, where you drop straight down<\/li>\r\n \t<li class=\"whitespace-normal break-words\">The cord stretch phase, where the bungee cord gradually slows your descent<\/li>\r\n<\/ul>\r\n<p class=\"whitespace-pre-wrap break-words\">For a [latex]150[\/latex]-meter jump height, the initial freefall distance is [latex]55[\/latex] meters before the cord begins to stretch. Let's calculate how long this freefall phase lasts using the physics equation for falling objects:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\Delta x = v_it + \\frac{1}{2}at^2[\/latex]<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">Where:<\/p>\r\n\r\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">[latex]\\Delta x[\/latex] is the freefall distance<\/li>\r\n \t<li class=\"whitespace-normal break-words\">[latex]v_i[\/latex] is the initial velocity<\/li>\r\n \t<li class=\"whitespace-normal break-words\">[latex]t[\/latex] is the time in seconds<\/li>\r\n \t<li class=\"whitespace-normal break-words\">[latex]a[\/latex] is the acceleration due to gravity<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31683[\/ohm2_question]<\/section>After experiencing the initial freefall, the jump enters an exciting new phase. The bungee cord begins to stretch and slow the descent. Then, like a giant elastic band, it launches upward! This creates a series of bounces, with each rebound becoming progressively smaller until eventually come to rest.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31684[\/ohm2_question]<\/section>\r\n<p class=\"whitespace-pre-wrap break-words\">Safety and equipment maintenance are crucial parts of bungee operations. At the end of each day, the bungee cords need to be carefully inspected, cleaned, and properly stored to maintain their reliability and elasticity.<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">At the Helsinki bungee site, Dana and Chen are responsible for this important safety task. Working independently:<\/p>\r\n\r\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Dana can complete the inspection and storage in [latex]3[\/latex] hours ([latex]180[\/latex] minutes)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Chen can complete the task in [latex]3[\/latex] hours and [latex]45[\/latex] minutes ([latex]225[\/latex] minutes)<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31685[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Build and use equations and formulas that aren&#8217;t straight lines to solve real-life problems.<\/li>\n<\/ul>\n<\/section>\n<p>In 2014, Margit Tall made history in Helsinki, Finland. At age [latex]95[\/latex], she became one of the oldest bungee jumpers in the world, taking a thrilling plunge from a crane [latex]150[\/latex] meters above the sea.<\/p>\n<figure id=\"attachment_6772\" aria-describedby=\"caption-attachment-6772\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6772 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-300x200.jpg\" alt=\"\" width=\"300\" height=\"200\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-300x200.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-1024x682.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-768x511.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-1536x1022.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-65x43.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-225x150.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving-350x233.jpg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16221251\/4.3_applications_and_inequalities_guy_diving.jpg 1600w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-6772\" class=\"wp-caption-text\">Photo of bungee jumping; Photo by Carlos Ruiz on Pexels<\/figcaption><\/figure>\n<p class=\"whitespace-pre-wrap break-words\">Before attempting a bungee jump, it&#8217;s crucial to understand the physics behind the experience. Each jump consists of two main phases:<\/p>\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">The freefall phase, where you drop straight down<\/li>\n<li class=\"whitespace-normal break-words\">The cord stretch phase, where the bungee cord gradually slows your descent<\/li>\n<\/ul>\n<p class=\"whitespace-pre-wrap break-words\">For a [latex]150[\/latex]-meter jump height, the initial freefall distance is [latex]55[\/latex] meters before the cord begins to stretch. Let&#8217;s calculate how long this freefall phase lasts using the physics equation for falling objects:<\/p>\n<p class=\"whitespace-pre-wrap break-words\" style=\"text-align: center;\">[latex]\\Delta x = v_it + \\frac{1}{2}at^2[\/latex]<\/p>\n<p class=\"whitespace-pre-wrap break-words\">Where:<\/p>\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">[latex]\\Delta x[\/latex] is the freefall distance<\/li>\n<li class=\"whitespace-normal break-words\">[latex]v_i[\/latex] is the initial velocity<\/li>\n<li class=\"whitespace-normal break-words\">[latex]t[\/latex] is the time in seconds<\/li>\n<li class=\"whitespace-normal break-words\">[latex]a[\/latex] is the acceleration due to gravity<\/li>\n<\/ul>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31683\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31683&theme=lumen&iframe_resize_id=ohm31683&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>After experiencing the initial freefall, the jump enters an exciting new phase. The bungee cord begins to stretch and slow the descent. Then, like a giant elastic band, it launches upward! This creates a series of bounces, with each rebound becoming progressively smaller until eventually come to rest.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31684\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31684&theme=lumen&iframe_resize_id=ohm31684&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p class=\"whitespace-pre-wrap break-words\">Safety and equipment maintenance are crucial parts of bungee operations. At the end of each day, the bungee cords need to be carefully inspected, cleaned, and properly stored to maintain their reliability and elasticity.<\/p>\n<p class=\"whitespace-pre-wrap break-words\">At the Helsinki bungee site, Dana and Chen are responsible for this important safety task. Working independently:<\/p>\n<ul class=\"-mt-1 [li&gt;&amp;]:mt-2 [li&gt;mark&gt;&amp;]:mt-2 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Dana can complete the inspection and storage in [latex]3[\/latex] hours ([latex]180[\/latex] minutes)<\/li>\n<li class=\"whitespace-normal break-words\">Chen can complete the task in [latex]3[\/latex] hours and [latex]45[\/latex] minutes ([latex]225[\/latex] minutes)<\/li>\n<\/ul>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31685\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31685&theme=lumen&iframe_resize_id=ohm31685&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":92,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1385"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":16,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1385\/revisions"}],"predecessor-version":[{"id":7619,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1385\/revisions\/7619"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/92"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1385\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1385"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1385"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1385"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}