{"id":54,"date":"2018-01-13T11:02:32","date_gmt":"2018-01-13T03:02:32","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=54"},"modified":"2018-01-13T11:02:32","modified_gmt":"2018-01-13T03:02:32","slug":"solving-projectile-motion-problems-resolve-initial-velocity-into-horizontal-and-vertical-components","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-resolve-initial-velocity-into-horizontal-and-vertical-components.htm","title":{"rendered":"Resolve initial velocity into horizontal and vertical components of projectile motion","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><a href=\"https:\/\/gurumuda.net\/physics\">Solved problems in projectile motion<\/a> &#8211; <a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-resolve-initial-velocity-into-horizontal-and-vertical-components.htm\">resolve initial velocity into horizontal and vertical components<\/a><\/p>\n<p style=\"text-align: justify\">1. A kicked football leaves the ground at an angle \u03b8 = 60<sup>o<\/sup> with a velocity of 10 m\/s. Calculate the initial velocity components!<br \/>\n<span style=\"text-decoration: underline\">Known :<\/span><br \/>\nAngle (\u03b8) = 60<sup>o<\/sup><br \/>\nInitial velocity (v<sub>o<\/sub>) = 10 m\/s<br \/>\n<span style=\"text-decoration: underline\">Wanted :<\/span> v<sub>ox<\/sub> dan v<sub>oy<\/sub><br \/>\n<span style=\"text-decoration: underline\">Solution :<\/span><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-56\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/01\/Solving-projectile-motion-problems-\u2013-resolve-initial-velocity-into-horizontal-and-vertical-components-1.png\" alt=\"Solving projectile motion problems \u2013 resolve initial velocity into horizontal and vertical components 1\" width=\"79\" height=\"136\" \/>Resolve the initial velocity into x component (horizontal) and y component (vertical).<br \/>\nsin \u03b8 = v<sub>oy<\/sub> \/ v<sub>o<\/sub> &#8212;&#8211;&gt; v<sub>oy<\/sub> = v<sub>o<\/sub> sin \u03b8<br \/>\ncos \u03b8 = v<sub>ox<\/sub> \/ v<sub>o<\/sub> &#8212;&#8211;&gt; v<sub>ox<\/sub> = v<sub>o<\/sub> cos \u03b8<\/p>\n<p style=\"text-align: justify\">x component (horizontal) :<br \/>\nv<sub>ox<\/sub> = v<sub>o<\/sub> cos \u03b8 = (10 m\/s)(cos 60<sup>o<\/sup>) = (10 m\/s)(0.5) = 5 m\/s<\/p>\n<p style=\"text-align: justify\">y component (vertical) :<br \/>\nv<sub>oy<\/sub> = v<sub>o<\/sub> sin \u03b8 = (10 m\/s)(sin 60<sup>o<\/sup>) = (10 m\/s)(0.5\u221a3) = 5\u221a3 m\/s<\/p>\n\n<p style=\"text-align: justify\">2. An object leaves ground at an angle \u03b8 = 30<sup>o<\/sup> with y component of the velocity 10 m\/s. Calculate initial velocity !<br \/>\n<span style=\"text-decoration: underline\">Known :<\/span><br \/>\nAngle (\u03b8) = 30<sup>o<\/sup><br \/>\ny component (v<sub>oy<\/sub>) = 10 m\/s<br \/>\n<span style=\"text-decoration: underline\">Wanted :<\/span> Initial velocity (v<sub>o<\/sub>)<br \/>\n<span style=\"text-decoration: underline\">Solution :<\/span><br \/>\nv<sub>oy<\/sub> = v<sub>o<\/sub> sin \u03b8<br \/>\n10 = (v<sub>o<\/sub>)(sin 30<sup>o<\/sup>)<br \/>\n10 = (v<sub>o<\/sub>)(0.5)<br \/>\nv<sub>o<\/sub> = 10 \/ 0.5<br \/>\nv<sub>o<\/sub> = 20 m\/s<\/p>\n\n<p style=\"text-align: justify\">3. Horizontal component of initial velocity is 30 m\/s and vertical component of initial velocity is 40 m\/s. Calculate initial velocity.<br \/>\n<span style=\"text-decoration: underline\">Known :<\/span><br \/>\nHorizontal component of initial velocity (v<sub>ox<\/sub>) = 30 m\/s<br \/>\nVertical component of initial velocity (v<sub>oy<\/sub>) = 40 m\/s<br \/>\n<span style=\"text-decoration: underline\">Wanted :<\/span> Initial velocity (v<sub>o<\/sub>)<br \/>\n<span style=\"text-decoration: underline\">Solution :<\/span><br \/>\nv<sub>o<\/sub><sup>2<\/sup> = v<sub>ox<\/sub><sup>2<\/sup> + v<sub>oy<\/sub><sup>2<\/sup> = 30<sup>2<\/sup> + 40<sup>2<\/sup> = 900 + 1600 = 2500<br \/>\nv<sub>o<\/sub> = \u221a2500<br \/>\nv<sub>o<\/sub> = 50 m\/s<\/p>\n\n<p style=\"text-align: justify\">4. A small ball projected horizontally with initial velocity v<sub>o<\/sub> = 6 m\/s. Calculate x component and y component of initial velocity.<br \/>\n<span style=\"text-decoration: underline\">Known :<\/span><br \/>\nInitial velocity (v<sub>o<\/sub>) = 6 m\/s<br \/>\n<span style=\"text-decoration: underline\">Wanted :<\/span> vox and v<sub>oy<\/sub><br \/>\n<span style=\"text-decoration: underline\">Solution :<\/span><br \/>\nBall move horizontally so that horizontal component of velocity (v<sub>ox<\/sub>) = initial velocity (v<sub>o<\/sub>) = 6 m\/s. Vertical component of velocity (v<sub>oy<\/sub>) = 0.<\/p>\n\n<p>[wpdm_package id=&#8217;545&#8242;]<\/p>\n<p align=\"justify\">[wpdm_package id=&#8217;536&#8242;]<\/p>\n<ol>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-resolve-initial-velocity-into-horizontal-and-vertical-components.htm\" rel=\"noopener\">Resolve initial velocity into horizontal and vertical components<\/a><\/li>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-determine-horizontal-displacement.htm\" rel=\"noopener\">Determine the horizontal displacement<\/a><\/li>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-determine-the-maximum-height.htm\" rel=\"noopener\">Determine the maximum height <\/a><\/li>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-determine-time-interval.htm\" rel=\"noopener\">Determine the time interval<\/a><\/li>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-determine-the-position-of-an-object.htm\" rel=\"noopener\">Determine the position of object<\/a><\/li>\n<li><a href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-determine-final-velocity.htm\" rel=\"noopener\">Determine the final velocity<\/a><\/li>\n<\/ol>\n<p><!--more--><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>Solved problems in projectile motion &#8211; resolve initial velocity into horizontal and vertical components 1. A kicked football leaves the ground at an angle \u03b8 = 60o with a velocity of 10 m\/s. Calculate the initial velocity components! Known : Angle (\u03b8) = 60o Initial velocity (vo) = 10 m\/s Wanted : vox dan voy &#8230; <a title=\"Resolve initial velocity into horizontal and vertical components of projectile motion\" class=\"read-more\" href=\"https:\/\/gurumuda.net\/physics\/solving-projectile-motion-problems-resolve-initial-velocity-into-horizontal-and-vertical-components.htm\" aria-label=\"Read more about Resolve initial velocity into horizontal and vertical components of projectile motion\">Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Resolve initial velocity into horizontal and vertical components of projectile motion","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-54","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/54","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=54"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/54\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=54"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=54"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}