{"id":3263,"date":"2018-05-16T10:05:29","date_gmt":"2018-05-16T04:35:29","guid":{"rendered":"http:\/\/www.aakash.ac.in\/blog\/?p=3263"},"modified":"2023-04-04T16:55:10","modified_gmt":"2023-04-04T11:25:10","slug":"what-is-projectile-motion","status":"publish","type":"post","link":"https:\/\/www.aakash.ac.in\/blog\/what-is-projectile-motion\/","title":{"rendered":"What is Projectile Motion?"},"content":{"rendered":"<p>Students appearing for <a href=\"https:\/\/goo.gl\/3Zq3jH\" target=\"_blank\" rel=\"noopener\"><strong>JEE main advanced\u00a0<\/strong><\/a>exam must prepare themselves thoroughly to secure a seat in any of the Indian Institutes of Technology (IITs). There is a vast amount of syllabus to be covered in the upcoming months. Students must sort out the subjects and topics by the marking scheme for each topic. All three subjects \u2013 Physics, Chemistry and Mathematics require an equal amount of time for preparation. However, it also depends on the extent of one\u2019s preparation and their strong and weak areas.<\/p>\n<p>Kinematics is one of the most important areas in Physics that a student must master thoroughly. The equations will come in handy throughout the entire year when they are studying physics, or even mathematics (vectors) for the matter of fact.<\/p>\n<p>Below is a short and simple wrap-up of projectile motion in Physics, that carries a good weight in the <strong>JEE main advanced<\/strong> exam.<\/p>\n<h2>What is a Projectile?<\/h2>\n<p>A projectile is a body (object) that is thrown into the space which is in flight and only gravity acts on it.<\/p>\n<h2>What is Projectile Motion?<\/h2>\n<p>Projectile motion is a form of motion that is experienced by an object that makes it move along a curved path due to the action of gravity. It is motion where the only force acting upon the object (projectile) is gravity. Also, when an object is in flight after being thrown, it is said to be in projectile motion.<\/p>\n<p><strong><u>Example<\/u><\/strong> \u2013A cricket ball or a javelin in the air.<\/p>\n<h2>What are the assumptions considered for Projectile Motion?<\/h2>\n<p>For projectile motion, the following assumptions are considered:<\/p>\n<ul>\n<li>The effect on the projectile is negligible due to the curvature of the Earth<\/li>\n<li>The impact on the projectile is insignificant due to the rotation of the Earth<\/li>\n<li>There is no resistance due to air<\/li>\n<\/ul>\n<p>Projectile motion has two simultaneous independent rectilinear motions:<\/p>\n<ul>\n<li>Along x-axis (Responsible for the horizontal motion of the object; uniform velocity)<\/li>\n<li>Along y-axis (Responsible for the vertical motion of the object; uniform downward acceleration \u2018g\u2019)<\/li>\n<\/ul>\n<h2>Equations of Motion for Constant Acceleration<\/h2>\n<p>The most commonly used equations for motion of an object with constant acceleration are:<\/p>\n<ol>\n<li><strong><em>v = u &#8211; gt<\/em><\/strong><\/li>\n<li><strong><em>s = ut \u2013 \u00bd gt<sup>2<\/sup><\/em><\/strong><\/li>\n<li><strong><em>v<sup>2<\/sup> = u<sup>2<\/sup> \u2013 2 gs<\/em><\/strong><\/li>\n<\/ol>\n<p>Here:<\/p>\n<ul>\n<li><strong><em>u = initial velocity<\/em><\/strong><\/li>\n<li><strong><em>g = acceleration due to gravity<\/em><\/strong><\/li>\n<li><strong><em>t = time<\/em><\/strong><\/li>\n<li><strong><em>s = displacement<\/em><\/strong><\/li>\n<li><strong><em>v = final velocity<\/em><\/strong><\/li>\n<\/ul>\n<h2>Equations for Projectile Motion<\/h2>\n<p>If a projectile is launched with velocity <em>\u2018u\u2019<\/em>, it makes an angle <em>\u2018\u03b8\u2019<\/em> with x-axis. Once the projectile is in the air, the acceleration acting on it due to gravity is directed vertically downwards:<\/p>\n<p>a= -g (combined)<\/p>\n<p>a<sub>x<\/sub> = 0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>A<\/u><\/em><\/strong><\/p>\n<p>a<sub>y<\/sub> = -g\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>B<\/u><\/em><\/strong><\/p>\n<p>Initial velocity <em>\u2018u\u2019 <\/em>is:<\/p>\n<p>u<sub>x<\/sub> = ucos\u03b8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>C<\/u><\/em><\/strong><\/p>\n<p>u<sub>y<\/sub> = usin\u03b8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>D<\/u><\/em><\/strong><\/p>\n<p>x and y = 0, if initial position is the origin of the projectile<\/p>\n<p>At any time <em>\u2018t\u2019<\/em>, displacement will be:<\/p>\n<p>x = (u<sub>x<\/sub>)t = (ucos\u03b8)t<\/p>\n<p>y = (usin\u03b8)t \u2013 (\u00bd)gt<sup>2\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/sup><strong><em><u>E<\/u><\/em><\/strong><\/p>\n<p>Velocity at time \u2018<em>t\u2019<\/em>can be obtained by:<\/p>\n<p>u<sub>x<\/sub> = ucos\u03b8<\/p>\n<p>u<sub>y<\/sub> = usin\u03b8\u2013 gt\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>F<\/u><\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>The relation between \u2018x\u2019 and \u2018y\u2019 can be further explained by:<\/p>\n<p>y= (tan\u03b8)x \u2013 gx<sup>2<\/sup>\/ (4u<sup>2<\/sup>cos<sup>2<\/sup>\u03b8) <strong><em><u>G<\/u><\/em><\/strong><\/p>\n<p><strong>Note: <\/strong><em>\u2018x\u2019<\/em> remains constant throughout the motion, and only \u2018<em>y<\/em>\u2019component changes.<\/p>\n<p><strong>Time of Flight<\/strong><\/p>\n<p>In equation G, the total time t<sub>f<\/sub>during the flight can be calculated by using y = 0. It means there is zero displacement in the vertical direction.<\/p>\n<p>t<sub>f<\/sub> = 2usin\u03b8\/g\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>H<\/u><\/em><\/strong><\/p>\n<p>t<sub>f<\/sub> is the time of the flight of the concerned projectile.<\/p>\n<p>t<sub>f<\/sub> = 2t<sub>m<\/sub>(t<sub>m<\/sub> is the time taken to reach maximum height)<\/p>\n<h4><strong>Maximum Height<\/strong><\/h4>\n<p>h<sub>max<\/sub> = (u<sup>2<\/sup>sin<sup>2<\/sup>\u03b8)\/2g<\/p>\n<p>The maximum height h<sub>m<\/sub>can be calculated by substituting t = t<sub>m<\/sub><\/p>\n<h4><strong>Range<\/strong><strong> of the Projectile<\/strong><\/h4>\n<p>Horizontal range (r) of the projectile is the distance covered by it from its initial position to the position where is passes y = 0.<\/p>\n<p>Horizontal Range = Horizontal component of velocity (u<sub>x<\/sub>) x Total Time of Flight (t)<\/p>\n<p>It is the distance traveled during the flight t<sub>f<\/sub><\/p>\n<p>r = ucos\u03b8 x (2usin\u03b8)\/g<\/p>\n<p>i.e.<\/p>\n<p>r = (u<sup>2<\/sup>sin(2\u03b8))\/g<\/p>\n<h2>The Equation of Trajectory (Why Projectile Motion is Parabolic)<\/h2>\n<p>Equations of motion tell us that:<\/p>\n<p>a = t(ucos\u03b8)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>K<\/u><\/em><\/strong><\/p>\n<p>b = usin\u03b8 x t \u2013 \u00bd x t<sup>2<\/sup>\/g\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em><u>L<\/u><\/em><\/strong><\/p>\n<p>where (a,b) is the position of a body at time (t)<\/p>\n<p>By taking Equation <strong><em><u>K<\/u><\/em><\/strong>and <strong><em><u>L<\/u><\/em><\/strong><\/p>\n<p>b = (atan\u03b8 \u2013 ga<sup>2<\/sup>)\/2u<sup>2<\/sup>cos<sup>2<\/sup>\u03b8 (Equation of Trajectory in Projectile Motion)<\/p>\n<p>Projectile motion is a two-dimensional motion. It can also be said that it is a form of motion in a plane.<\/p>\n<table style=\"font-family: arial, sans-serif; border: 1px solid black; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"border: 1px solid black; padding-left: 10px; background-color: #ffffff; text-align: center;\">\n<p style=\"text-align: left;\">Aakash Education Services Limited is now on <em><a style=\"color: #ff0000;\" href=\"https:\/\/bit.ly\/2WRN8Ay\" target=\"_blank\" rel=\"noopener\">Telegram<\/a><\/em>. To get all the latest information, tips &amp; tricks, answer solutions for the latest ongoing exams. Subscribe to Aakash on <em><a style=\"color: #ff0000;\" href=\"https:\/\/bit.ly\/2WRN8Ay\" target=\"_blank\" rel=\"noopener\">Telegram<\/a><\/em>.<\/p>\n<p style=\"text-align: left;\">Subscribe to our <em><a style=\"color: #ff0000;\" href=\"https:\/\/bit.ly\/3bVdDJU\" target=\"_blank\" rel=\"noopener\">Youtube<\/a><\/em> channel.<\/p>\n<\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Students appearing for JEE main advanced\u00a0exam must prepare themselves thoroughly to secure a seat in any of the Indian Institutes of Technology (IITs). There is a vast amount of syllabus to be covered in the upcoming months. Students must sort out the subjects and topics by the marking scheme for each topic. All three subjects [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":3264,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1400],"tags":[754,752,753],"class_list":["post-3263","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news-and-events","tag-equations-for-projectile-motion","tag-projectile-motion","tag-science-topic"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is Projectile Motion?<\/title>\n<meta name=\"description\" content=\"What is Projectile Motion?: Students appearing for JEE main advanced\u00a0exam must prepare themselves thoroughly to secure a seat in any of the Indian Institutes of Technology (IITs)\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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I am Kriti, a graduate in Education and Literature, bringing over 11 years of experience as an expert news writer and content creator. With more than 7 years dedicated to Aakash Educational Services, I excel in crafting compelling narratives that not only grab readers' attention but also inspire them to take action. I believe that great content should inform and motivate, making me passionate about helping others understand the nuances of content marketing. Always eager to stay ahead of the curve, I actively seek out emerging trends in digital marketing and content strategy, ensuring my work remains relevant and impactful. Collaboration is at the heart of my approach; I enjoy working with teams to develop content strategies that align with organizational goals, fostering a creative and effective environment. Beyond my professional pursuits, I love travelling and dancing. 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