{"id":199666,"date":"2025-03-12T08:58:20","date_gmt":"2025-03-12T08:58:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199666"},"modified":"2025-03-12T08:58:22","modified_gmt":"2025-03-12T08:58:22","slug":"a-stone-is-dropped-from-the-roof-of-a-high-building-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/a-stone-is-dropped-from-the-roof-of-a-high-building-3\/","title":{"rendered":"A stone is dropped from the roof of a high building"},"content":{"rendered":"\n<p>A stone is dropped from the roof of a high building. A second stone is dropped 1.50 s later. How far apart are the stones when the second one has reached a speed of 12.0 m\/s?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The two stones are <strong>29.04 meters<\/strong> apart when the second stone reaches a speed of 12.0 m\/s.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding the motion<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The stones are in <strong>free fall<\/strong>, meaning they only experience acceleration due to gravity (<strong>( g = 9.81 \\, m\/s^2 )<\/strong>).<\/li>\n\n\n\n<li>The first stone is dropped from rest.<\/li>\n\n\n\n<li>The second stone is dropped <strong>1.5 seconds later<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding time for the second stone<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The second stone accelerates uniformly under gravity. Using the equation for velocity:<br>[<br>v = g t<br>]<br>Substituting ( v = 12.0 \\, m\/s ):<br>[<br>12.0 = 9.81 t_2<br>]<br>Solving for ( t_2 ):<br>[<br>t_2 = \\frac{12.0}{9.81} = 1.22 \\text{ s}<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding distance fallen<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The displacement of a freely falling object is given by:<br>[<br>d = \\frac{1}{2} g t^2<br>]<\/li>\n\n\n\n<li>For the <strong>second stone<\/strong>:<br>[<br>d_2 = \\frac{1}{2} (9.81) (1.22)^2<br>]<br>[<br>d_2 = 7.32 \\text{ m}<br>]<\/li>\n\n\n\n<li>The <strong>first stone<\/strong> has fallen for ( t_1 = 1.22 + 1.5 = 2.72 ) seconds:<br>[<br>d_1 = \\frac{1}{2} (9.81) (2.72)^2<br>]<br>[<br>d_1 = 36.36 \\text{ m}<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding the separation<\/strong>:<br>[<br>\\text{Distance apart} = d_1 &#8211; d_2<br>]<br>[<br>= 36.36 &#8211; 7.32<br>]<br>[<br>= 29.04 \\text{ m}<br>]<\/li>\n<\/ol>\n\n\n\n<p>Thus, when the second stone reaches a speed of <strong>12.0 m\/s<\/strong>, the two stones are <strong>29.04 meters apart<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A stone is dropped from the roof of a high building. A second stone is dropped 1.50 s later. How far apart are the stones when the second one has reached a speed of 12.0 m\/s? The correct answer and explanation is : The two stones are 29.04 meters apart when the second stone reaches [&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-199666","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199666","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=199666"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199666\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}