{"id":280012,"date":"2025-08-04T13:19:43","date_gmt":"2025-08-04T13:19:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280012"},"modified":"2025-08-04T13:19:45","modified_gmt":"2025-08-04T13:19:45","slug":"a-ball-is-dropped-from-a-height-of-16-meters-and-bounces-back-to-3-4-of-its-previous-height-each-time","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/a-ball-is-dropped-from-a-height-of-16-meters-and-bounces-back-to-3-4-of-its-previous-height-each-time\/","title":{"rendered":"A ball is dropped from a height of 16 meters and bounces back to 3\/4 of its previous height each time"},"content":{"rendered":"\n

A ball is dropped from a height of 16 meters and bounces back to 3\/4 of its previous height each time<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

This is an example of a geometric series problem. A ball is dropped from a height of 16 meters and bounces back to 3\/4 of its previous height each time.<\/p>\n\n\n\n

To find the total distance the ball travels, we can break it down into two parts:<\/p>\n\n\n\n

    \n
  1. Initial fall<\/strong>: The ball falls 16 meters initially.<\/li>\n\n\n\n
  2. Subsequent bounces<\/strong>: After hitting the ground, the ball bounces back to 3\/4 of its previous height. Therefore, the ball goes up to 12 meters, then falls back down the same distance, and continues this pattern.<\/li>\n<\/ol>\n\n\n\n

    The total distance traveled is the sum of the following:<\/p>\n\n\n\n

      \n
    • The first fall: 16 meters<\/li>\n\n\n\n
    • The first bounce up and down: 2 * (3\/4 * 16) = 24 meters<\/li>\n\n\n\n
    • The second bounce up and down: 2 * (3\/4 * 3\/4 * 16) = 18 meters<\/li>\n\n\n\n
    • The third bounce up and down: 2 * (3\/4 * 3\/4 * 3\/4 * 16) = 13.5 meters<\/li>\n<\/ul>\n\n\n\n

      The series continues indefinitely, with each term being 3\/4 of the previous one.<\/p>\n\n\n\n

      To find the total distance traveled, we sum the infinite geometric series for the bounces. The sum of an infinite geometric series is given by the formula: S=a1\u2212rS = \\frac{a}{1 – r}<\/p>\n\n\n\n

      where a<\/em> is the first term and r<\/em> is the common ratio.<\/p>\n\n\n\n

      In this case:<\/p>\n\n\n\n

        \n
      • a<\/em> is 16 (the first drop).<\/li>\n\n\n\n
      • r<\/em> is 3\/4 (the bounce ratio).<\/li>\n<\/ul>\n\n\n\n

        The total distance traveled for the bounces is: S=161\u22123\/4=161\/4=64S = \\frac{16}{1 – 3\/4} = \\frac{16}{1\/4} = 64<\/p>\n\n\n\n

        Thus, the total distance traveled is: 16+64=80 meters16 + 64 = 80 \\text{ meters}<\/p>\n\n\n\n

        So, the total distance the ball travels is 80 meters.<\/p>\n\n\n\n

          <\/ol>\n","protected":false},"excerpt":{"rendered":"

          A ball is dropped from a height of 16 meters and bounces back to 3\/4 of its previous height each time The correct answer and explanation is: This is an example of a geometric series problem. A ball is dropped from a height of 16 meters and bounces back to 3\/4 of its previous height […]<\/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-280012","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280012","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=280012"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280012\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}