{"id":266185,"date":"2025-07-22T16:45:41","date_gmt":"2025-07-22T16:45:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266185"},"modified":"2025-07-22T16:45:46","modified_gmt":"2025-07-22T16:45:46","slug":"a-soccer-ball-is-kicked-at-72-0-km-h-at-20o-above-horizon","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/a-soccer-ball-is-kicked-at-72-0-km-h-at-20o-above-horizon\/","title":{"rendered":"A soccer ball is kicked at 72.0 km\/h at 20o above horizon"},"content":{"rendered":"\n<p>A soccer ball is kicked at 72.0 km\/h at 20o above horizon. How far from initial spot it was kicked, is the ball 2.00 m above the ground? (the question was given to us like this, unsure of what it means asking if the ball is 2m above ground)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to break the motion of the soccer ball into horizontal and vertical components and apply the kinematic equations of projectile motion.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert Units and Set Up Variables<\/h3>\n\n\n\n<p>First, convert the speed from km\/h to m\/s:72.0\u2009km\/h=72.0\u00d710003600\u2009m\/s=20.0\u2009m\/s72.0 \\, \\text{km\/h} = \\frac{72.0 \\times 1000}{3600} \\, \\text{m\/s} = 20.0 \\, \\text{m\/s}72.0km\/h=360072.0\u00d71000\u200bm\/s=20.0m\/s<\/p>\n\n\n\n<p>We are given the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial speed (v0v_0v0\u200b) = 20.0 m\/s<\/li>\n\n\n\n<li>Angle of launch (\u03b8\\theta\u03b8) = 20\u00b0<\/li>\n\n\n\n<li>Gravitational acceleration (ggg) = 9.81 m\/s\u00b2<\/li>\n\n\n\n<li>Vertical displacement (yyy) = 2.00 m (we need to check if the ball is 2 m above the ground)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Resolve Initial Velocity into Components<\/h3>\n\n\n\n<p>The initial velocity components are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Horizontal velocity:<\/li>\n<\/ul>\n\n\n\n<p>v0x=v0cos\u2061(\u03b8)=20.0\u00d7cos\u2061(20\u2218)=20.0\u00d70.9397=18.794\u2009m\/sv_{0x} = v_0 \\cos(\\theta) = 20.0 \\times \\cos(20^\\circ) = 20.0 \\times 0.9397 = 18.794 \\, \\text{m\/s}v0x\u200b=v0\u200bcos(\u03b8)=20.0\u00d7cos(20\u2218)=20.0\u00d70.9397=18.794m\/s<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vertical velocity:<\/li>\n<\/ul>\n\n\n\n<p>v0y=v0sin\u2061(\u03b8)=20.0\u00d7sin\u2061(20\u2218)=20.0\u00d70.3420=6.840\u2009m\/sv_{0y} = v_0 \\sin(\\theta) = 20.0 \\times \\sin(20^\\circ) = 20.0 \\times 0.3420 = 6.840 \\, \\text{m\/s}v0y\u200b=v0\u200bsin(\u03b8)=20.0\u00d7sin(20\u2218)=20.0\u00d70.3420=6.840m\/s<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find Time When the Ball is 2 m Above the Ground<\/h3>\n\n\n\n<p>The equation for vertical displacement is:y=v0yt\u221212gt2y = v_{0y} t &#8211; \\frac{1}{2} g t^2y=v0y\u200bt\u221221\u200bgt2<\/p>\n\n\n\n<p>Substituting y=2.00y = 2.00y=2.00 m, v0y=6.840v_{0y} = 6.840v0y\u200b=6.840 m\/s, and g=9.81g = 9.81g=9.81 m\/s\u00b2:2.00=6.840t\u221212(9.81)t22.00 = 6.840t &#8211; \\frac{1}{2}(9.81)t^22.00=6.840t\u221221\u200b(9.81)t2<\/p>\n\n\n\n<p>This is a quadratic equation:4.905t2\u22126.840t+2.00=04.905t^2 &#8211; 6.840t + 2.00 = 04.905t2\u22126.840t+2.00=0<\/p>\n\n\n\n<p>Using the quadratic formula:t=\u2212(\u22126.840)\u00b1(\u22126.840)2\u22124(4.905)(2.00)2(4.905)t = \\frac{-(-6.840) \\pm \\sqrt{(-6.840)^2 &#8211; 4(4.905)(2.00)}}{2(4.905)}t=2(4.905)\u2212(\u22126.840)\u00b1(\u22126.840)2\u22124(4.905)(2.00)\u200b\u200bt=6.840\u00b146.786\u221239.249.81t = \\frac{6.840 \\pm \\sqrt{46.786 &#8211; 39.24}}{9.81}t=9.816.840\u00b146.786\u221239.24\u200b\u200bt=6.840\u00b17.5469.81t = \\frac{6.840 \\pm \\sqrt{7.546}}{9.81}t=9.816.840\u00b17.546\u200b\u200bt=6.840\u00b12.759.81t = \\frac{6.840 \\pm 2.75}{9.81}t=9.816.840\u00b12.75\u200b<\/p>\n\n\n\n<p>So, two possible values for time:t1=6.840+2.759.81=9.5909.81=0.978\u2009st_1 = \\frac{6.840 + 2.75}{9.81} = \\frac{9.590}{9.81} = 0.978 \\, \\text{s}t1\u200b=9.816.840+2.75\u200b=9.819.590\u200b=0.978st2=6.840\u22122.759.81=4.0909.81=0.417\u2009st_2 = \\frac{6.840 &#8211; 2.75}{9.81} = \\frac{4.090}{9.81} = 0.417 \\, \\text{s}t2\u200b=9.816.840\u22122.75\u200b=9.814.090\u200b=0.417s<\/p>\n\n\n\n<p>We take the larger time, t1=0.978t_1 = 0.978t1\u200b=0.978 s, because this is when the ball reaches 2 m for the second time during its flight.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find Horizontal Distance<\/h3>\n\n\n\n<p>Now, we can find the horizontal distance by using the formula:x=v0x\u00d7tx = v_{0x} \\times tx=v0x\u200b\u00d7tx=18.794\u2009m\/s\u00d70.978\u2009s=18.41\u2009mx = 18.794 \\, \\text{m\/s} \\times 0.978 \\, \\text{s} = 18.41 \\, \\text{m}x=18.794m\/s\u00d70.978s=18.41m<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The soccer ball will be 2.00 m above the ground at a horizontal distance of <strong>18.41 m<\/strong> from the initial spot where it was kicked.<\/p>\n\n\n\n<p>This confirms the horizontal distance when the ball is at 2 m height. The question likely wants to know where along its trajectory the ball is exactly 2 m above the ground.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1553.jpeg\" alt=\"\" class=\"wp-image-266186\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A soccer ball is kicked at 72.0 km\/h at 20o above horizon. How far from initial spot it was kicked, is the ball 2.00 m above the ground? (the question was given to us like this, unsure of what it means asking if the ball is 2m above ground) The Correct Answer and Explanation is: [&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-266185","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266185","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=266185"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}