{"id":188674,"date":"2025-02-07T08:02:18","date_gmt":"2025-02-07T08:02:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188674"},"modified":"2025-02-07T08:02:20","modified_gmt":"2025-02-07T08:02:20","slug":"romeo-is-throwing-pebbles-gently-up-to-juliets-window-and-he-wants-the-pebbles-to-hit-the-window-with-only-a-horizontal-component-of-velocity","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/07\/romeo-is-throwing-pebbles-gently-up-to-juliets-window-and-he-wants-the-pebbles-to-hit-the-window-with-only-a-horizontal-component-of-velocity\/","title":{"rendered":"Romeo is throwing pebbles gently up to Juliet\u2019s window, and he wants the pebbles to hit the window with only a horizontal component of velocity"},"content":{"rendered":"\n

Romeo is throwing pebbles gently up to Juliet\u2019s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 8.0 m below her window and 8.5 m from the base of the wall (Fig. 3\u201349). How fast are the pebbles going when they hit her window?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

To determine the velocity of the pebbles when they hit Juliet’s window with only a horizontal component of velocity, we can break this down into two main parts: the vertical and horizontal motion of the pebble.<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • Vertical distance (height from Romeo to Juliet\u2019s window) = 8.0 m.<\/li>\n\n\n\n
  • Horizontal distance = 8.5 m.<\/li>\n\n\n\n
  • Acceleration due to gravity, ( g = 9.8 \\, m\/s^2 ).<\/li>\n\n\n\n
  • Initial vertical velocity ( v_{y0} = 0 ) m\/s (since Romeo is throwing the pebble horizontally).<\/li>\n<\/ul>\n\n\n\n

    Step 1: Vertical motion<\/h3>\n\n\n\n

    Since the pebbles hit the window with no vertical velocity component, the pebble must first fall and then reverse its trajectory by only having a horizontal component upon impact. This implies the vertical velocity is zero at the time the pebble reaches the window.<\/p>\n\n\n\n

    For vertical motion, we can use the following kinematic equation:<\/p>\n\n\n\n

    [
    y = v_{y0} t + \\frac{1}{2} g t^2
    ]<\/p>\n\n\n\n

    Given that ( v_{y0} = 0 ) and ( y = 8.0 \\, m ), we have:<\/p>\n\n\n\n

    [
    8.0 = \\frac{1}{2} g t^2
    ]<\/p>\n\n\n\n

    Solving for ( t ) (time to hit the window):<\/p>\n\n\n\n

    [
    8.0 = \\frac{1}{2} (9.8) t^2
    ]
    [
    t^2 = \\frac{8.0 \\times 2}{9.8}
    ]
    [
    t^2 = 1.6327 \\quad \\Rightarrow \\quad t = 1.278 \\, s
    ]<\/p>\n\n\n\n

    Step 2: Horizontal motion<\/h3>\n\n\n\n

    Now, using the time ( t = 1.278 \\, s ), we can calculate the horizontal velocity required for the pebble to travel a horizontal distance of 8.5 m. Since there is no horizontal acceleration (assuming no air resistance), we use the equation:<\/p>\n\n\n\n

    [
    x = v_x t
    ]<\/p>\n\n\n\n

    where ( x = 8.5 \\, m ), and solving for ( v_x ):<\/p>\n\n\n\n

    [
    v_x = \\frac{x}{t} = \\frac{8.5}{1.278} = 6.65 \\, m\/s
    ]<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    Thus, the horizontal velocity of the pebbles when they hit the window is 6.65 m\/s<\/strong>. This means that Romeo must throw the pebbles with a speed of 6.65 m\/s in the horizontal direction to ensure they reach Juliet’s window with only a horizontal velocity component.<\/p>\n\n\n\n

    This solution assumes that the pebble is only subject to gravity in the vertical direction and that air resistance is negligible.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Romeo is throwing pebbles gently up to Juliet\u2019s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 8.0 m below her window and 8.5 m from the base of the wall (Fig. 3\u201349). How fast are the […]<\/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-188674","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188674","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=188674"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188674\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188674"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188674"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}