{"id":191236,"date":"2025-02-14T10:35:38","date_gmt":"2025-02-14T10:35:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191236"},"modified":"2025-02-14T10:35:40","modified_gmt":"2025-02-14T10:35:40","slug":"at-an-instant-when-a-soccer-ball-is-in-contact-with-the-foot-of-the-player-kicking-it","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/at-an-instant-when-a-soccer-ball-is-in-contact-with-the-foot-of-the-player-kicking-it\/","title":{"rendered":"At an instant when a soccer ball is in contact with the foot of the player kicking it"},"content":{"rendered":"\n<p>At an instant when a soccer ball is in contact with the foot of the player kicking it, the horizontal or x component of the ball&#8217;s acceleration is 810 m\/s\u00b2 and the vertical or y component of its acceleration is 760 m\/s\u00b2. The ball&#8217;s mass is 0.42 kg. What is the magnitude of the net force acting on the soccer ball at this instant? Number i Save for Later Units Attempts: 0 of 1 used Submit Answer<\/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 calculate the magnitude of the net force acting on the soccer ball, we need to use Newton&#8217;s second law of motion, which states that:<\/p>\n\n\n\n<p>[<br>F_{\\text{net}} = m \\cdot a<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( F_{\\text{net}} ) is the net force acting on the object,<\/li>\n\n\n\n<li>( m ) is the mass of the object (in this case, the soccer ball),<\/li>\n\n\n\n<li>( a ) is the acceleration of the object.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the acceleration components<\/h3>\n\n\n\n<p>We are given the horizontal (x) and vertical (y) components of acceleration:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a_x = 810 \\, \\text{m\/s}^2 ),<\/li>\n\n\n\n<li>( a_y = 760 \\, \\text{m\/s}^2 ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the resultant acceleration<\/h3>\n\n\n\n<p>The resultant (or total) acceleration ( a ) can be found by combining the horizontal and vertical components using the Pythagorean theorem:<\/p>\n\n\n\n<p>[<br>a = \\sqrt{a_x^2 + a_y^2}<br>]<\/p>\n\n\n\n<p>Substituting the given values:<\/p>\n\n\n\n<p>[<br>a = \\sqrt{(810)^2 + (760)^2}<br>]<br>[<br>a = \\sqrt{656100 + 577600}<br>]<br>[<br>a = \\sqrt{1235700}<br>]<br>[<br>a \\approx 1111.2 \\, \\text{m\/s}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the net force<\/h3>\n\n\n\n<p>Now that we have the magnitude of the acceleration, we can use Newton&#8217;s second law to find the net force. The mass of the soccer ball is given as 0.42 kg, so:<\/p>\n\n\n\n<p>[<br>F_{\\text{net}} = m \\cdot a<br>]<br>[<br>F_{\\text{net}} = 0.42 \\, \\text{kg} \\cdot 1111.2 \\, \\text{m\/s}^2<br>]<br>[<br>F_{\\text{net}} \\approx 466.7 \\, \\text{N}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The magnitude of the net force acting on the soccer ball at this instant is approximately <strong>467 N<\/strong>.<\/p>\n\n\n\n<p>This calculation assumes that the horizontal and vertical components of acceleration are independent of each other and that the ball is being acted upon by an external force (the player&#8217;s foot) that results in these accelerations. The net force is the combination of these two components, which is why we used the Pythagorean theorem to find the total acceleration.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At an instant when a soccer ball is in contact with the foot of the player kicking it, the horizontal or x component of the ball&#8217;s acceleration is 810 m\/s\u00b2 and the vertical or y component of its acceleration is 760 m\/s\u00b2. The ball&#8217;s mass is 0.42 kg. What is the magnitude of the net [&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-191236","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191236","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=191236"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191236\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}