{"id":215278,"date":"2025-05-16T16:28:00","date_gmt":"2025-05-16T16:28:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=215278"},"modified":"2025-05-16T16:28:02","modified_gmt":"2025-05-16T16:28:02","slug":"in-an-experiment-two-identical-rocks-are-simultaneously-thrown-from-the-edge-of-a-cliff-a-distance-h0-above-the-ground","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-ground\/","title":{"rendered":"In an experiment two identical rocks are simultaneously thrown from the edge of a cliff a distance h0 above the ground"},"content":{"rendered":"\n

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

(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

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer (Velocity vs. Time Graph Explanation)<\/strong><\/h3>\n\n\n\n

To sketch the velocity vs. time graph<\/strong> for both Rock A and Rock B:<\/p>\n\n\n\n

    \n
  • Use a vertical axis for velocity (v)<\/strong> and a horizontal axis for time (t)<\/strong>.<\/li>\n\n\n\n
  • Let upward be positive<\/strong>, so gravity<\/strong> will cause a negative acceleration<\/strong> of \u2212g (\u22129.8 m\/s\u00b2)<\/strong>.<\/li>\n\n\n\n
  • Both rocks are thrown from the same height<\/strong> and at the same speed (v\u2080)<\/strong>, one upward and the other downward.<\/li>\n<\/ul>\n\n\n\n

    Key Events and Labels<\/strong>:<\/h4>\n\n\n\n
      \n
    • Rock A:<\/li>\n\n\n\n
    • Starts at +v\u2080<\/strong> (positive, upward velocity).<\/li>\n\n\n\n
    • Slows down due to gravity, reaches 0 velocity at the top<\/strong> of its path at t = \u00bdtA<\/strong>, then starts falling downward.<\/li>\n\n\n\n
    • Continues to accelerate downward and becomes negative in velocity.<\/li>\n\n\n\n
    • Hits the ground at t = tA<\/strong> with a larger magnitude<\/strong> of velocity than it started with.<\/li>\n\n\n\n
    • Rock B:<\/li>\n\n\n\n
    • Starts at \u2212v\u2080<\/strong> (negative, downward velocity).<\/li>\n\n\n\n
    • Continues to accelerate downward at \u2212g<\/strong>.<\/li>\n\n\n\n
    • Hits the ground sooner than rock A, at t = tB < tA<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      On the graph:<\/p>\n\n\n\n

        \n
      1. Rock A<\/strong>: A straight line starting at +v\u2080<\/strong> on the velocity axis, decreasing linearly due to gravity (slope = \u2212g), reaching 0 at t = \u00bdtA<\/strong>, and then becoming negative, ending at a more negative velocity at t = tA<\/strong>.<\/li>\n\n\n\n
      2. Rock B<\/strong>: A straight line starting at \u2212v\u2080<\/strong>, with the same slope<\/strong> (\u2212g) as Rock A, but since it doesn’t go upward first, it hits the ground at t = tB<\/strong>, which is earlier than tA<\/strong>.<\/li>\n<\/ol>\n\n\n\n

        Both lines should be straight with equal slopes because gravity affects both identically.<\/p>\n\n\n\n

        \n\n\n\n

        Explanation (300+ words)<\/strong><\/h3>\n\n\n\n

        This experiment is a classic physics problem involving one-dimensional motion under constant acceleration (gravity). The key insight is that both rocks experience the same acceleration<\/strong> due to gravity (g \u2248 9.8 m\/s\u00b2 downward), but they are thrown in opposite directions initially \u2014 one upward (Rock A) and one downward (Rock B).<\/p>\n\n\n\n

        For Rock A<\/strong>, it is thrown upward with an initial velocity of +v\u2080<\/strong>. Since gravity acts downward, it slows the rock until its vertical velocity becomes 0 m\/s at the peak<\/strong> of its path. This point occurs at t = \u00bdtA<\/strong>. Afterward, the rock begins falling back down, gaining speed in the negative<\/strong> (downward) direction due to gravity. By the time it hits the ground at t = tA<\/strong>, its velocity is negative and greater in magnitude than +v\u2080 due to the total distance it has traveled (up and then down past the starting point).<\/p>\n\n\n\n

        For Rock B<\/strong>, it is thrown downward with an initial velocity of \u2212v\u2080<\/strong>. Gravity accelerates it further downward. Since it does not need to first reverse direction, it hits the ground before Rock A<\/strong>, at t = tB < tA<\/strong>. Its velocity continues becoming more negative due to gravity\u2019s constant downward pull.<\/p>\n\n\n\n

        The velocity vs. time graph<\/strong> for both rocks are straight lines with the same slope<\/strong> (\u2212g). The difference lies in their starting points and duration<\/strong>. Rock A\u2019s graph starts at +v\u2080 and passes through zero at t = \u00bdtA, while Rock B starts at \u2212v\u2080 and ends sooner. The intersection at t = \u00bdtA on Rock A\u2019s graph represents the moment it changes direction.<\/p>\n\n\n\n

        This graph visually demonstrates how symmetric vertical motion is under constant acceleration and emphasizes the importance of direction in velocity.<\/p>\n","protected":false},"excerpt":{"rendered":"

        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 […]<\/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-215278","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215278","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=215278"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215278\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=215278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=215278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=215278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}