{"id":8109,"date":"2020-06-28T08:43:12","date_gmt":"2020-06-28T12:43:12","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=8109"},"modified":"2024-10-05T18:09:20","modified_gmt":"2024-10-05T22:09:20","slug":"moving-reference-frames-aircraft-problem","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/moving-reference-frames-aircraft-problem\/","title":{"rendered":"Moving reference frames &#8211; aircraft problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7787 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/mrfs-300x233.png\" alt=\"\" width=\"303\" height=\"182\" \/><\/p>\n<p>Aircraft A and B are flying on the same horizontal plane, each with a constant speed. Aircraft A is traveling on a straight path, whereas the path of B is circular.\u00a0We are interested in understanding how the motion of one aircraft is viewed by a passenger on the other aircraft.<\/p>\n<p><strong><em>Stationary observer<\/em><\/strong><br \/>\nShown below is an animation of the motion of A and B as seen by a stationary observer. The paths of A and B are straight and circular, as expected.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/section_03A_01.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>View of B as seen by an observer on A<\/em><\/strong><br \/>\nShown below is an animation of the motion of aircraft B as seen by a passenger on aircraft A. The path of B is no longer circular, as expected. Can you see this in the relative motion equation for (<strong><em>v<\/em><\/strong><sub>B\/A<\/sub>)<sub>rel<\/sub>\u00a0?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/section_03A_01A.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>View of A as seen by an observer on B<\/em><\/strong><br \/>\nShown below is an animation of the motion of aircraft A as seen by a passenger on aircraft B. The path of A is no longer straight, as expected. Can you see this in the relative motion equation for (<strong><em>v<sub>A\/B<\/sub><\/em><\/strong>)<sub>rel<\/sub>\u00a0?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/section_03A_01B.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><em><strong>NOTE<\/strong><\/em>:<br \/>\nRecall from before that when the observer is not rotating, then (<strong><em>v<sub>A\/B<\/sub><\/em><\/strong>)<sub>rel<\/sub>\u00a0 = -(<strong><em>v<sub>B\/A<\/sub><\/em><\/strong>)<sub>rel<\/sub>\u00a0. In the case, an observer on B IS rotating, and as we can see in these animations, these two observed velocities differ by much more than a sign.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aircraft A and B are flying on the same horizontal plane, each with a constant speed. Aircraft A is traveling on a straight path, whereas the path of B is circular.\u00a0We are interested in understanding how the motion of one aircraft is viewed by a passenger on the other aircraft. Stationary observer Shown below is &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/moving-reference-frames-aircraft-problem\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Moving reference frames &#8211; aircraft problem<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-8109","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/comments?post=8109"}],"version-history":[{"count":4,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8109\/revisions"}],"predecessor-version":[{"id":8118,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8109\/revisions\/8118"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=8109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}