{"id":179409,"date":"2024-12-30T19:54:47","date_gmt":"2024-12-30T19:54:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179409"},"modified":"2024-12-30T19:54:50","modified_gmt":"2024-12-30T19:54:50","slug":"rebecca-is-flying-a-drone-at-a-constant-height","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/12\/30\/rebecca-is-flying-a-drone-at-a-constant-height\/","title":{"rendered":"Rebecca is flying a drone at a constant height"},"content":{"rendered":"\n<p>Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18m every 3s. After 5s, the drone is at a height of 40m. The drone&#8217;s height in meters, y, is a function of the time in seconds, x.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given a problem in which Rebecca is flying a drone at a constant height and then decides to make it rise vertically. The drone&#8217;s height, yy, is a function of time, xx, and we are tasked with finding this relationship.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understand the given information<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The drone rises 18 meters every 3 seconds. This means the drone has a vertical speed of: Rate\u00a0of\u00a0rise=18\u00a0meters3\u00a0seconds=6\u00a0meters\u00a0per\u00a0second.\\text{Rate of rise} = \\frac{18 \\text{ meters}}{3 \\text{ seconds}} = 6 \\text{ meters per second}.<\/li>\n\n\n\n<li>After 5 seconds, the drone&#8217;s height is 40 meters. This provides a specific point on the function: when x=5x = 5, y=40y = 40.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Set up the general function<\/h3>\n\n\n\n<p>The drone&#8217;s height increases at a constant rate of 6 meters per second, so the function describing the height, yy, as a function of time, xx, will be linear. A linear function is of the form: y=mx+b,y = mx + b,<\/p>\n\n\n\n<p>where mm is the slope (rate of change of height) and bb is the y-intercept (initial height when x=0x = 0).<\/p>\n\n\n\n<p>From the information given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slope m=6m = 6 meters per second (since the drone rises 6 meters every second).<\/li>\n\n\n\n<li>The equation for height becomes: y=6x+b.y = 6x + b.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Use the point (5,40)(5, 40) to find bb<\/h3>\n\n\n\n<p>We are told that after 5 seconds, the height is 40 meters, i.e., when x=5x = 5, y=40y = 40. We can substitute these values into the equation to solve for bb: 40=6(5)+b.40 = 6(5) + b. 40=30+b.40 = 30 + b. b=40\u221230=10.b = 40 &#8211; 30 = 10.<\/p>\n\n\n\n<p>Thus, the equation for the drone\u2019s height as a function of time is: y=6x+10.y = 6x + 10.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Interpretation<\/h3>\n\n\n\n<p>The function y=6x+10y = 6x + 10 tells us that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The drone\u2019s height increases by 6 meters for every second that passes.<\/li>\n\n\n\n<li>When x=0x = 0 (at the start), the drone is at a height of 10 meters.<\/li>\n\n\n\n<li>After 5 seconds, the drone reaches a height of 40 meters, as given in the problem.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The height of the drone as a function of time is y=6x+10y = 6x + 10. This equation accurately models the drone&#8217;s vertical motion based on the given information.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18m every 3s. After 5s, the drone is at a height of 40m. The drone&#8217;s height in meters, y, is a function of the time in seconds, x. The correct answer and explanation is: We are [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-179409","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=179409"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179409\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}