{"id":199544,"date":"2025-03-12T05:31:19","date_gmt":"2025-03-12T05:31:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199544"},"modified":"2025-03-12T05:31:21","modified_gmt":"2025-03-12T05:31:21","slug":"a-window-washer-drops-a-bucket-from-his-perch-on-a-tall-building","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/a-window-washer-drops-a-bucket-from-his-perch-on-a-tall-building\/","title":{"rendered":"A window washer drops a bucket from his perch on a tall building"},"content":{"rendered":"\n<p>A window washer drops a bucket from his perch on a tall building. Through her window, an accountant in an office on a lower floor sees the bucket fall. It takes 0.30 s to fall past her window that is 2.2 m tall.<br>How high is the window washer above the bottom of her window?<br>What is the velocity of the bucket when it reaches the bottom of the window?<\/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>Let&#8217;s solve this step by step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given data:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time taken to pass the window: ( t = 0.30 ) s<\/li>\n\n\n\n<li>Height of the window: ( h = 2.2 ) m<\/li>\n\n\n\n<li>Acceleration due to gravity: ( g = 9.81 ) m\/s\u00b2<\/li>\n<\/ul>\n\n\n\n<p>We need to find:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The velocity of the bucket at the bottom of the window.<\/li>\n\n\n\n<li>The height from which the bucket was dropped.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Finding the velocity at the bottom of the window<\/h3>\n\n\n\n<p>Using the <strong>kinematic equation<\/strong> for uniformly accelerated motion:<\/p>\n\n\n\n<p>[<br>h = v_i t + \\frac{1}{2} g t^2<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( h = 2.2 ) m<\/li>\n\n\n\n<li>( t = 0.30 ) s<\/li>\n\n\n\n<li>( g = 9.81 ) m\/s\u00b2<\/li>\n\n\n\n<li>( v_i ) is the velocity of the bucket at the top of the window.<\/li>\n<\/ul>\n\n\n\n<p>Rearrange to solve for ( v_i ):<\/p>\n\n\n\n<p>[<br>v_i = \\frac{h &#8211; \\frac{1}{2} g t^2}{t}<br>]<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>[<br>v_i = \\frac{2.2 &#8211; \\frac{1}{2} (9.81) (0.30)^2}{0.30}<br>]<\/p>\n\n\n\n<p>[<br>v_i = \\frac{2.2 &#8211; 0.44145}{0.30} = \\frac{1.75855}{0.30} = 5.86 \\text{ m\/s}<br>]<\/p>\n\n\n\n<p>Now, using the velocity equation:<\/p>\n\n\n\n<p>[<br>v_f = v_i + g t<br>]<\/p>\n\n\n\n<p>[<br>v_f = 5.86 + (9.81 \\times 0.30)<br>]<\/p>\n\n\n\n<p>[<br>v_f = 5.86 + 2.943 = 8.80 \\text{ m\/s}<br>]<\/p>\n\n\n\n<p>So, the <strong>velocity of the bucket at the bottom of the window<\/strong> is <strong>8.80 m\/s<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Finding the height of the window washer<\/h3>\n\n\n\n<p>The bucket starts from rest, so using:<\/p>\n\n\n\n<p>[<br>v_i^2 = 2 g h&#8217;<br>]<\/p>\n\n\n\n<p>[<br>h&#8217; = \\frac{v_i^2}{2g} = \\frac{(5.86)^2}{2 (9.81)}<br>]<\/p>\n\n\n\n<p>[<br>h&#8217; = \\frac{34.34}{19.62} = 1.75 \\text{ m}<br>]<\/p>\n\n\n\n<p>Thus, the <strong>window washer is 1.75 m above the top of the window<\/strong>, or <strong>3.95 m above the bottom of the window<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-900.png\" alt=\"\" class=\"wp-image-199545\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A window washer drops a bucket from his perch on a tall building. Through her window, an accountant in an office on a lower floor sees the bucket fall. It takes 0.30 s to fall past her window that is 2.2 m tall.How high is the window washer above the bottom of her window?What is [&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-199544","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199544","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=199544"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199544\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}