{"id":215275,"date":"2025-05-16T16:21:26","date_gmt":"2025-05-16T16:21:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=215275"},"modified":"2025-05-16T16:21:27","modified_gmt":"2025-05-16T16:21:27","slug":"in-an-experiment-two-identical-rocks-are-simultaneously-thrown-from-the-edge-of-a-cliff-a-distance-h0-above-the-groud","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/16\/in-an-experiment-two-identical-rocks-are-simultaneously-thrown-from-the-edge-of-a-cliff-a-distance-h0-above-the-groud\/","title":{"rendered":"In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance h0 above the groud."},"content":{"rendered":"\n<p>In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance h0 above the ground. Rock A is thrown vertically upward with speed v0 and rock B is thrown vertically downward with speed v0. Rock A and rock B strike the ground at times tA and tB, respectively. Consider the positive vertical direction to be upward.<\/p>\n\n\n\n<p>(a) On the axes given below, sketch and label graphs of the velocity as a function of time for rock A and rock B. Label the time tB. Times tA and 1\/2tA are given on the graph.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we analyze the motion of two identical rocks thrown from the same height but with different initial velocities. One is thrown <strong>upward<\/strong> (rock A) and the other <strong>downward<\/strong> (rock B), both with the same speed v0v_0. We&#8217;re asked to sketch their <strong>velocity vs. time<\/strong> graphs and explain the motion.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>Understanding the Motion<\/strong>:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Rock A (Thrown Upward)<\/strong>:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial velocity: +v0+v_0 (positive because it&#8217;s upward).<\/li>\n\n\n\n<li>Due to gravity, the rock slows down at a rate of gg (approximately 9.8\u2009m\/s29.8 \\, \\text{m\/s}^2) until it reaches its highest point.<\/li>\n\n\n\n<li>At the <strong>top<\/strong>, its velocity is <strong>0<\/strong>.<\/li>\n\n\n\n<li>Then it starts to fall downward, accelerating at gg, so its velocity becomes <strong>negative<\/strong>.<\/li>\n\n\n\n<li>It continues accelerating until it hits the ground at time tAt_A.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Rock B (Thrown Downward)<\/strong>:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial velocity: \u2212v0-v_0 (negative because it&#8217;s downward).<\/li>\n\n\n\n<li>It accelerates in the <strong>same direction<\/strong> as its motion, so its speed increases.<\/li>\n\n\n\n<li>It reaches the ground at an earlier time tBt_B, where tB&lt;tAt_B &lt; t_A, because it didn\u2019t first travel upward.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcc8 <strong>Velocity vs. Time Graph<\/strong>:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>vertical axis<\/strong> is velocity (m\/s), with positive values above and negative below.<\/li>\n\n\n\n<li>The <strong>horizontal axis<\/strong> is time, starting from 0.<\/li>\n\n\n\n<li>For both rocks, the velocity changes linearly with time due to constant acceleration by gravity.<\/li>\n<\/ul>\n\n\n\n<p><strong>Rock A<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Starts at +v0+v_0, decreases linearly.<\/li>\n\n\n\n<li>Crosses velocity = 0 (top of its flight) at time tA2\\frac{t_A}{2}.<\/li>\n\n\n\n<li>Continues to become more negative until time tAt_A.<\/li>\n<\/ul>\n\n\n\n<p><strong>Rock B<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Starts at \u2212v0-v_0, becomes more negative linearly.<\/li>\n\n\n\n<li>Hits the ground at tBt_B, which is <strong>before<\/strong> tAt_A.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccd On the graph:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rock A\u2019s line starts at +v0+v_0, slopes down through 0 at tA2\\frac{t_A}{2}, ends at a large negative value at tAt_A.<\/li>\n\n\n\n<li>Rock B\u2019s line starts at \u2212v0-v_0, slopes downward (more negative), and ends at tBt_B, which is <strong>between 0 and tAt_A<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Conclusion<\/strong>:<\/h3>\n\n\n\n<p>This graph illustrates that <strong>gravity affects both rocks equally<\/strong>, but rock A takes longer due to its upward motion first. Both lines are straight (constant acceleration), and the key difference is the <strong>starting velocity<\/strong> and <strong>total time before hitting the ground<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance h0 above the ground. Rock A is thrown vertically upward with speed v0 and rock B is thrown vertically downward with speed v0. Rock A and rock B strike the ground at times tA and tB, respectively. Consider [&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-215275","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215275","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=215275"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215275\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=215275"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=215275"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=215275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}