{"id":182401,"date":"2025-01-13T18:38:02","date_gmt":"2025-01-13T18:38:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182401"},"modified":"2025-01-13T18:38:05","modified_gmt":"2025-01-13T18:38:05","slug":"a-rocket-initially-at-rest-launched-vertically-from-a-ground-with-an-acceleration-of-20-m-s2-for-6-0s-until-its-engine-stops","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/13\/a-rocket-initially-at-rest-launched-vertically-from-a-ground-with-an-acceleration-of-20-m-s2-for-6-0s-until-its-engine-stops\/","title":{"rendered":"A Rocket initially at rest, launched vertically from a ground with an acceleration of 20 m\/s2 for 6.0s until its engine stops"},"content":{"rendered":"\n<p>A Rocket initially at rest, launched vertically from a ground with an acceleration of 20 m\/s2 for 6.0s until its engine stops. Disregarding any air resistance, calculate what is the maximum height above the ground the rocket achieved? ( Hint: after the stop of engine the rocket continues to move under acceleration of gravity)<\/p>\n\n\n\n<p>a.<\/p>\n\n\n\n<p>0.79km<\/p>\n\n\n\n<p>b.<\/p>\n\n\n\n<p>1.9km<\/p>\n\n\n\n<p>c.<\/p>\n\n\n\n<p>0.8km<\/p>\n\n\n\n<p>d.<\/p>\n\n\n\n<p>0.73km<\/p>\n\n\n\n<p>e.<\/p>\n\n\n\n<p>1.1km<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s break down the problem step by step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Analyze the rocket&#8217;s motion during the engine-powered phase (0 to 6 seconds)<\/h3>\n\n\n\n<p>The rocket starts from rest and accelerates vertically with a constant acceleration of 20 m\/s\u00b2 for 6.0 seconds. We can calculate the velocity at the end of this phase using the equation: v=u+atv = u + at<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>uu is the initial velocity, which is 0 m\/s (since the rocket starts from rest),<\/li>\n\n\n\n<li>aa is the acceleration, 20 m\/s\u00b2,<\/li>\n\n\n\n<li>tt is the time, 6.0 seconds.<\/li>\n<\/ul>\n\n\n\n<p>v=0+(20)(6)=120\u2009m\/sv = 0 + (20)(6) = 120 \\, \\text{m\/s}<\/p>\n\n\n\n<p>So, the velocity of the rocket when the engine stops is 120 m\/s.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the height at the end of the engine-powered phase<\/h3>\n\n\n\n<p>We can find the displacement (height) during the acceleration phase using the following equation: s=ut+12at2s = ut + \\frac{1}{2} a t^2<\/p>\n\n\n\n<p>Substitute the values: s=0\u00d76+12\u00d720\u00d762=0+0.5\u00d720\u00d736=360\u2009ms = 0 \\times 6 + \\frac{1}{2} \\times 20 \\times 6^2 = 0 + 0.5 \\times 20 \\times 36 = 360 \\, \\text{m}<\/p>\n\n\n\n<p>So, the rocket travels 360 meters during the 6 seconds of engine-powered flight.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Analyze the motion after the engine stops (6 seconds onward)<\/h3>\n\n\n\n<p>Once the engine stops, the rocket moves upward under the influence of gravity alone, so the acceleration is now \u22129.8\u2009m\/s2-9.8 \\, \\text{m\/s}^2. The velocity at the start of this phase is 120 m\/s, and the rocket will continue to rise until its velocity reaches zero.<\/p>\n\n\n\n<p>Using the equation v2=u2+2asv^2 = u^2 + 2as, where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>v=0v = 0 m\/s (final velocity when it stops),<\/li>\n\n\n\n<li>u=120u = 120 m\/s (initial velocity at engine stop),<\/li>\n\n\n\n<li>a=\u22129.8a = -9.8 m\/s\u00b2 (acceleration due to gravity),<\/li>\n\n\n\n<li>ss is the displacement during this phase.<\/li>\n<\/ul>\n\n\n\n<p>0=1202+2(\u22129.8)s0 = 120^2 + 2(-9.8)s 0=14400\u221219.6s0 = 14400 &#8211; 19.6s 19.6s=1440019.6s = 14400 s=1440019.6=734.69\u2009ms = \\frac{14400}{19.6} = 734.69 \\, \\text{m}<\/p>\n\n\n\n<p>So, the rocket will rise 734.69 meters after the engine stops.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Total maximum height<\/h3>\n\n\n\n<p>The total maximum height is the sum of the height during the powered phase and the height during the coasting phase: Total&nbsp;height=360\u2009m+734.69\u2009m=1094.69\u2009m\u22481.1\u2009km\\text{Total height} = 360 \\, \\text{m} + 734.69 \\, \\text{m} = 1094.69 \\, \\text{m} \\approx 1.1 \\, \\text{km}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The maximum height the rocket achieves is approximately <strong>1.1 km<\/strong>, which corresponds to option <strong>e<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Rocket initially at rest, launched vertically from a ground with an acceleration of 20 m\/s2 for 6.0s until its engine stops. Disregarding any air resistance, calculate what is the maximum height above the ground the rocket achieved? ( Hint: after the stop of engine the rocket continues to move under acceleration of gravity) a. [&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-182401","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182401","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=182401"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182401\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}