To solve this problem, we analyze the motion of both stones using kinematic equations. The motion of both stones follows free fall, meaning their acceleration is due to gravity, ( g = 9.81 \\, \\text{m\/s}^2 ).<\/p>\n\n\n\n
Step 1: Determine the Time for the Second Stone<\/h3>\n\n\n\n
We use the velocity equation for free fall:
[
v = g t
]
Solving for ( t ) when the second stone reaches a speed of 12.0 m\/s:
[
t = \\frac{v}{g} = \\frac{12.0}{9.81} = 1.22 \\text{ s}
]
So, the second stone has been falling for 1.22 seconds.<\/p>\n\n\n\n
Step 2: Find the Distance Fallen by Each Stone<\/h3>\n\n\n\n
The displacement of a freely falling object is given by:
[
y = \\frac{1}{2} g t^2
]<\/p>\n\n\n\n
Distance Fallen by the Second Stone:<\/h4>\n\n\n\n
[
y_2 = \\frac{1}{2} (9.81) (1.22)^2
]
[
y_2 = 7.30 \\text{ m}
]<\/p>\n\n\n\n
Distance Fallen by the First Stone:<\/h4>\n\n\n\n
Since the first stone was dropped 1.50 s earlier, its total fall time is:
[
t_1 = 1.22 + 1.50 = 2.72 \\text{ s}
]
Using the displacement equation:
[
y_1 = \\frac{1}{2} (9.81) (2.72)^2
]
[
y_1 = 36.3 \\text{ m}
]<\/p>\n\n\n\n
Step 3: Find the Distance Between the Two Stones<\/h3>\n\n\n\n
[
\\Delta y = y_1 – y_2 = 36.3 – 7.30 = 29.0 \\text{ m}
]<\/p>\n\n\n\n
So, when the second stone reaches a speed of 12.0 m\/s, the two stones are 29.0 meters apart<\/strong>.<\/p>\n\n\n\n Here is an illustration showing the two stones being dropped from a tall building, with the first stone farther down and the second one higher up but accelerating downward. The vertical separation of 29.0 meters is marked between them.<\/p>\n","protected":false},"excerpt":{"rendered":" A stone is dropped from the roof of a high building. A second stone is dropped 1.50 s later. How far apart are the stones when the second one has reached a speed of 12.0 m\/s? The correct answer and explanation is : To solve this problem, we analyze the motion of both stones using […]<\/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-199298","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199298","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=199298"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199298\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-831.png\")
<\/figure>\n\n\n\n