{"id":152465,"date":"2024-10-11T10:15:04","date_gmt":"2024-10-11T10:15:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152465"},"modified":"2024-10-11T10:15:07","modified_gmt":"2024-10-11T10:15:07","slug":"a-stone-is-dropped-from-the-top-of-a-tower","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/11\/a-stone-is-dropped-from-the-top-of-a-tower\/","title":{"rendered":"A stone is dropped from the top of a tower"},"content":{"rendered":"\n<p>A stone is dropped from the top of a tower. The stone hits the ground after 5 seconds. Find the height of the tower and the velocity with which the stone hits the ground.<\/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>To determine the height of the tower and the velocity with which the stone hits the ground, we can use the equations of motion under uniform acceleration due to gravity.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time (t) = 5 seconds<\/li>\n\n\n\n<li>Acceleration due to gravity (g) \u2248 9.81 m\/s\u00b2 (we can use 10 m\/s\u00b2 for simplicity)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">1. Height of the Tower<\/h3>\n\n\n\n<p>The formula to calculate the distance (height) an object falls freely from rest is:<\/p>\n\n\n\n<p>[<br>h = \\frac{1}{2} g t^2<br>]<\/p>\n\n\n\n<p>Substituting the known values:<\/p>\n\n\n\n<p>[<br>h = \\frac{1}{2} \\times 10 \\, \\text{m\/s}^2 \\times (5 \\, \\text{s})^2<br>]<\/p>\n\n\n\n<p>Calculating further:<\/p>\n\n\n\n<p>[<br>h = \\frac{1}{2} \\times 10 \\times 25 = \\frac{250}{2} = 125 \\, \\text{meters}<br>]<\/p>\n\n\n\n<p>Thus, the height of the tower is <strong>125 meters<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Velocity with Which the Stone Hits the Ground<\/h3>\n\n\n\n<p>To find the final velocity (v) of the stone just before it hits the ground, we use the formula:<\/p>\n\n\n\n<p>[<br>v = g t<br>]<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>[<br>v = 10 \\, \\text{m\/s}^2 \\times 5 \\, \\text{s} = 50 \\, \\text{m\/s}<br>]<\/p>\n\n\n\n<p>Therefore, the velocity with which the stone hits the ground is <strong>50 m\/s<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary<\/h3>\n\n\n\n<p>In summary, after dropping a stone from the top of a tower for 5 seconds, the height of the tower is calculated to be 125 meters, and the final velocity of the stone upon impact with the ground is 50 m\/s. This analysis is based on the principles of free fall under gravity, illustrating how time and gravitational acceleration affect the distance fallen and the velocity attained.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A stone is dropped from the top of a tower. The stone hits the ground after 5 seconds. Find the height of the tower and the velocity with which the stone hits the ground. The Correct Answer and Explanation is : To determine the height of the tower and the velocity with which the stone [&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-152465","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152465","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=152465"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152465\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}