{"id":274159,"date":"2025-07-28T05:48:11","date_gmt":"2025-07-28T05:48:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=274159"},"modified":"2025-07-28T05:48:15","modified_gmt":"2025-07-28T05:48:15","slug":"a-child-boards-a-bus-for-summer-camp","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/a-child-boards-a-bus-for-summer-camp\/","title":{"rendered":"A child boards a bus for summer camp"},"content":{"rendered":"\n<p>A child boards a bus for summer camp. His mom is waiting next to the bus. The bus begins moving 3 m\/s east with respect to the ground. The child is walking 0.5 m\/s west towards the back of the bus with respect to the bus. The mother begins running 1 m\/s east with respect to the ground, chasing after the bus and thoroughly humiliating her child. What is the child\u2019s velocity a) relative to the ground? b) relative to the mother?<\/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<h3 class=\"wp-block-heading\">Part a) Child\u2019s Velocity Relative to the Ground<\/h3>\n\n\n\n<p>To find the child&#8217;s velocity relative to the ground, we need to consider both the motion of the bus and the child&#8217;s motion within the bus.<\/p>\n\n\n\n<p>The bus is moving east with a velocity of 3 m\/s relative to the ground. The child, however, is walking towards the back of the bus (westward) at 0.5 m\/s relative to the bus. Since the bus is moving east and the child is moving west within the bus, we subtract the child&#8217;s velocity from the bus&#8217;s velocity to find the child&#8217;s velocity relative to the ground.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Velocity of the bus relative to the ground = 3 m\/s east<\/li>\n\n\n\n<li>Velocity of the child relative to the bus = 0.5 m\/s west (which is negative relative to the bus&#8217;s direction)<\/li>\n<\/ul>\n\n\n\n<p>Thus, the child&#8217;s velocity relative to the ground is: Child\u2019s&nbsp;velocity&nbsp;relative&nbsp;to&nbsp;the&nbsp;ground=3\u2009m\/s\u22120.5\u2009m\/s=2.5\u2009m\/s&nbsp;east\\text{Child&#8217;s velocity relative to the ground} = 3 \\, \\text{m\/s} &#8211; 0.5 \\, \\text{m\/s} = 2.5 \\, \\text{m\/s east}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part b) Child\u2019s Velocity Relative to the Mother<\/h3>\n\n\n\n<p>Next, we calculate the child\u2019s velocity relative to the mother, who is running east at 1 m\/s relative to the ground. The child&#8217;s velocity relative to the ground is 2.5 m\/s east, as calculated earlier, and the mother\u2019s velocity relative to the ground is 1 m\/s east.<\/p>\n\n\n\n<p>To find the relative velocity between the child and the mother, we subtract the mother&#8217;s velocity from the child&#8217;s velocity relative to the ground: Child\u2019s&nbsp;velocity&nbsp;relative&nbsp;to&nbsp;the&nbsp;mother=2.5\u2009m\/s&nbsp;east\u22121\u2009m\/s&nbsp;east=1.5\u2009m\/s&nbsp;east\\text{Child\u2019s velocity relative to the mother} = 2.5 \\, \\text{m\/s east} &#8211; 1 \\, \\text{m\/s east} = 1.5 \\, \\text{m\/s east}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>a) The child\u2019s velocity relative to the ground is 2.5 m\/s east.<br>b) The child\u2019s velocity relative to the mother is 1.5 m\/s east.<\/p>\n\n\n\n<p>In this situation, the mother is chasing after the bus and, despite her efforts, the child is still moving east at a faster rate than her.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A child boards a bus for summer camp. His mom is waiting next to the bus. The bus begins moving 3 m\/s east with respect to the ground. The child is walking 0.5 m\/s west towards the back of the bus with respect to the bus. The mother begins running 1 m\/s east with respect [&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-274159","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274159","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=274159"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274159\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=274159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=274159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=274159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}