{"id":212106,"date":"2025-05-05T17:06:36","date_gmt":"2025-05-05T17:06:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=212106"},"modified":"2025-05-05T17:06:37","modified_gmt":"2025-05-05T17:06:37","slug":"as-a-tennis-ball-is-struck","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/05\/as-a-tennis-ball-is-struck\/","title":{"rendered":"As a tennis ball is struck"},"content":{"rendered":"\n<p>As a tennis ball is struck, it departs from the racket horizontally with a speed of 28.0 m\/s. The ball hits the court at a horizontal distance of 19.6 m from the racket. Draw the figure in the space provided below and, showing your work, answer the following questions:<\/p>\n\n\n\n<p>(a)Determine the initial velocity of the ball in the x- and y-direction.<br>(b) What is the acceleration of the ball in the x- and y-direction?<br>(c) How much time does the ball spend in air?<br>(d) How far above the court is the tennis ball when it leaves the racket?<br>(e) What is the x-component of the ball\u2019s velocity when the ball hits the court?<br>(f) What is the y-component of the ball\u2019s velocity when the ball hits the court?<br>(g) What is the velocity when the ball hits the court?<\/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<h3 class=\"wp-block-heading\">Given Information:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The initial horizontal velocity of the ball, $v_x = 28.0 \\, \\text{m\/s}$.<\/li>\n\n\n\n<li>The horizontal distance the ball travels, $x = 19.6 \\, \\text{m}$.<\/li>\n<\/ul>\n\n\n\n<p>We need to find the velocity components and other parameters of the ball&#8217;s motion.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Determine the initial velocity of the ball in the x- and y-direction.<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Initial velocity in the x-direction, $v_{x0}$:<\/strong><\/li>\n\n\n\n<li>The horizontal velocity remains constant because there is no horizontal acceleration (neglecting air resistance).<\/li>\n\n\n\n<li>Hence, $v_{x0} = 28.0 \\, \\text{m\/s}$.<\/li>\n\n\n\n<li><strong>Initial velocity in the y-direction, $v_{y0}$:<\/strong><\/li>\n\n\n\n<li>Since the ball is struck horizontally, there is no initial vertical velocity.<\/li>\n\n\n\n<li>Therefore, $v_{y0} = 0 \\, \\text{m\/s}$.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">(b) What is the acceleration of the ball in the x- and y-direction?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Acceleration in the x-direction, $a_x$:<\/strong><\/li>\n\n\n\n<li>In the absence of air resistance, the horizontal velocity does not change.<\/li>\n\n\n\n<li>Hence, $a_x = 0 \\, \\text{m\/s}^2$.<\/li>\n\n\n\n<li><strong>Acceleration in the y-direction, $a_y$:<\/strong><\/li>\n\n\n\n<li>The only force acting vertically on the ball is gravity, causing a downward acceleration.<\/li>\n\n\n\n<li>Therefore, $a_y = -9.8 \\, \\text{m\/s}^2$.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">(c) How much time does the ball spend in the air?<\/h3>\n\n\n\n<p>The time of flight can be determined by considering the vertical motion. Since the ball was struck horizontally, its initial vertical velocity is zero.<\/p>\n\n\n\n<p>Using the equation for vertical displacement:<\/p>\n\n\n\n<p>$$<br>y = v_{y0} t + \\frac{1}{2} a_y t^2<br>$$<\/p>\n\n\n\n<p>Since $y = 0$ (the ball returns to the court), we get:<\/p>\n\n\n\n<p>$$<br>0 = 0 + \\frac{1}{2} (-9.8) t^2<br>$$<\/p>\n\n\n\n<p>Simplifying:<\/p>\n\n\n\n<p>$$<br>t^2 = \\frac{2y}{g}<br>$$<\/p>\n\n\n\n<p>Since the ball starts at some height $y_0$ above the court (which we will later find), we need a different approach to solve for time. First we&#8217;ll solve the equation numerically<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As a tennis ball is struck, it departs from the racket horizontally with a speed of 28.0 m\/s. The ball hits the court at a horizontal distance of 19.6 m from the racket. Draw the figure in the space provided below and, showing your work, answer the following questions: (a)Determine the initial velocity of the [&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-212106","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212106","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=212106"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212106\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=212106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=212106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=212106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}