{"id":641,"date":"2024-07-12T08:02:44","date_gmt":"2024-07-12T08:02:44","guid":{"rendered":"https:\/\/www.meniit.com\/study-material\/?p=641"},"modified":"2024-10-04T05:01:36","modified_gmt":"2024-10-04T05:01:36","slug":"relative-motion-in-river-flow","status":"publish","type":"post","link":"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow","title":{"rendered":"Relative Motion in River Flow"},"content":{"rendered":"<p style=\"text-align: justify;\">If a man can swim relative to water with velocity <i><span style=\"font-style: italic;\">V<\/span><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>mR<\/sub> and water is flowing relative to ground with velocity <i><span style=\"font-style: italic;\">V<\/span><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>R<\/sub>, velocity of man relative to ground <i><span style=\"font-style: italic;\">V<\/span><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>m<\/sub> will be given by :<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-642 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-river-flow-e1720765933283.png\" alt=\"relative motion in river flow\" width=\"840\" height=\"78\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-river-flow-e1720765933283.png 840w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-river-flow-e1720765933283-300x28.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/relative-motion-in-river-flow-e1720765933283-768x71.png 768w\" sizes=\"auto, (max-width: 840px) 100vw, 840px\" \/><\/p>\n<h2 style=\"text-align: justify;\">Downstream &amp; Upstream Swimming<\/h2>\n<p style=\"text-align: justify;\">Velocity of river is u and velocity of man in still water is v.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-647 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/downstream-swimming.png\" alt=\"downstream swimming\" width=\"800\" height=\"110\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/downstream-swimming.png 800w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/downstream-swimming-300x41.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/downstream-swimming-768x106.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-644 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/upstream-swimming.png\" alt=\"upstream swimming\" width=\"799\" height=\"108\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/upstream-swimming.png 799w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/upstream-swimming-300x41.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/upstream-swimming-768x104.png 768w\" sizes=\"auto, (max-width: 799px) 100vw, 799px\" \/><\/p>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p>A swimmer capable of swimming with velocity \u2018v\u2019 relative to water jumps in a flowing river having velocity \u2018u\u2019. The man swims a distance d down stream and returns back to the original position. Find out the time taken in complete motion.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/downstream-upstream-swimming-1.png\" alt=\"least distance of long sighted\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow\/#Motion-of-Man-while-crossing-a-river\" title=\"Motion of Man while crossing a river\">Motion of Man while crossing a river<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow\/#Drift\" title=\"Drift\">Drift<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow\/#Crossing-the-river-in-shortest-time\" title=\"Crossing the river in shortest time\">Crossing the river in shortest time<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow\/#Crossing-the-river-in-shortest-path-Minimum-Drift\" title=\"Crossing the river in shortest path, Minimum Drift\">Crossing the river in shortest path, Minimum Drift<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Motion-of-Man-while-crossing-a-river\"><\/span>Motion of Man while crossing a river<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Consider a man swimming in a river with a velocity of <i><span style=\"font-style: italic;\">V<\/span><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>MR<\/sub> relative to river at an angle of \u03b8 with the river flow. The velocity of river is <i><span style=\"font-style: italic;\">V<\/span><span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex;\">\u2192<\/span><\/i><sub>R<\/sub> . Let there be two observers I and II.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-651 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-Man-while-crossing-river-e1720766189292.png\" alt=\"Motion of Man while crossing a river\" width=\"808\" height=\"263\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-Man-while-crossing-river-e1720766189292.png 808w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-Man-while-crossing-river-e1720766189292-300x98.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/Motion-of-Man-while-crossing-river-e1720766189292-768x250.png 768w\" sizes=\"auto, (max-width: 808px) 100vw, 808px\" \/><\/p>\n<p style=\"text-align: justify;\">Hence the swimmer will appear to move at an angle \u03b8&#8217; with the river flow.<\/p>\n<ul>\n<li>Motion of swimmer for observer I<\/li>\n<li>Motion of swimmer for observer II<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The motion observed by the observer I is same as the motion with respect to the ground frame of reference.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-653 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1.png\" alt=\"formula\" width=\"436\" height=\"73\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1.png 436w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-1-300x50.png 300w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" \/><\/p>\n<p style=\"text-align: justify;\">Here v<sub>MR<\/sub> sin\u03b8 is the component of velocity of man in the direction perpendicular to the river flow. This component of velocity is responsible for the man crossing the river. Hence if the time to cross the river is t,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-655 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/velocity.png\" alt=\"velocity\" width=\"196\" height=\"68\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Drift\"><\/span>Drift<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">It is defined as the displacement of man in the direction of river flow. It is simply the displacement along x-axis, during the period the man crosses the river.<br \/>\n(v<sub>MR<\/sub> cos \u03b8 + v<sub>R<\/sub>) is the component of velocity of man in the direction of river flow and this component of velocity is responsible for drift along the river flow. If drift is x then,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-656 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/drift.png\" alt=\"drift \" width=\"279\" height=\"96\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Crossing-the-river-in-shortest-time\"><\/span>Crossing the river in shortest time<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-659 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/crossing-river.png\" alt=\"crossing river\" width=\"811\" height=\"122\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/crossing-river.png 811w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/crossing-river-300x45.png 300w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/crossing-river-768x116.png 768w\" sizes=\"auto, (max-width: 811px) 100vw, 811px\" \/><\/p>\n<div style=\"padding: 10px; background-color: #d4effc;\">\n<h4 style=\"margin: 10px; padding: 10px; color: #005197;\">Note:<\/h4>\n<p>In the case of crossing the river in shortest time there will be drift along x direction.<\/p>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Crossing-the-river-in-shortest-path-Minimum-Drift\"><\/span>Crossing the river in shortest path, Minimum Drift<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The minimum possible drift is zero. In this case the man swims in the direction perpendicular to the river flow as seen from the ground. This path is known as <strong>shortest path<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-661 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/shortest-path.png\" alt=\"shortest path\" width=\"408\" height=\"92\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/shortest-path.png 408w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/shortest-path-300x68.png 300w\" sizes=\"auto, (max-width: 408px) 100vw, 408px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-662 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift.png\" alt=\"minimum drift \" width=\"748\" height=\"350\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift.png 748w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/minimum-drift-300x140.png 300w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\" \/><\/p>\n<p>&nbsp;<\/p>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p>A 400 m wide river is flowing at a rate of 2.0 m\/s. A boat is sailing with a velocity of 10 m\/s with respect to the water, in a direction perpendicular to the river.<\/p>\n<p>(a) Find the time taken by the boat to reach the opposite bank.<\/p>\n<p>(b) How far from the point directly opposite to the starting point does the boat reach the opposite bank?<\/p>\n<p>(c) In what direction does the boat actually move, with river flow (downstream).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/solution.png\" alt=\"least distance of long sighted\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p>A man can swim at the rate of 5 km\/h in still water. A 1 km wide river flows at the rate of 3 km\/h<br \/>\nThe man wishes to swim across the river directly opposite to the starting point.<\/p>\n<p>(a) Along what direction must the man swim?<\/p>\n<p>(b) What should be his resultant velocity?<\/p>\n<p>(c) How much time will he take to cross the river?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/10\/solution.png\" alt=\"least distance of long sighted\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div style=\"margin: 5px; padding: 10px; background-color: #fbdfed;\">\n<h4 id=\"example-solution\" style=\"color: #cc1d74;\"><strong>Example :\u00a0<\/strong><\/h4>\n<p style=\"text-align: justify;\">A river is following from west to east at a speed of 5 metres\/minute. A boy on the south bank of river, capable of swimming at 10 metres\/minute in still water, wants to swim across the river in the shortest time, (i) Find the direction in which he should swim, (ii) Find the direction when drift along the river is zero.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-550 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/slutions.png\" alt=\"least distance of long sighted\" width=\"923\" height=\"372\" \/><\/p>\n<\/div>\n<div class=\"newspaper-x-tags\"><strong>TAGS: <\/strong><span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/downstream-upstream-swimming\" rel=\"tag\">Downstream &amp; Upstream Swimming<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/drift\" rel=\"tag\">Drift<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-of-man-while-crossing-a-river\" rel=\"tag\">Motion of Man while crossing a river<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/relative-motion-in-river-flow\" rel=\"tag\">Relative Motion in River Flow<\/a> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>If a man can swim relative to water with velocity V\u2192mR and water is flowing relative to ground with velocity&nbsp;&nbsp;&#8230;.<a class=\"read_more\" href=\"https:\/\/www.meniit.com\/study-material\/jee\/class-xith\/11th-physics\/relative-motion-in-river-flow\" rel=\"nofollow\">Read More >><\/a><\/p>\n","protected":false},"author":5,"featured_media":1127,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"rank_math_lock_modified_date":false,"footnotes":""},"categories":[255,254,253],"tags":[265,267,266,264],"class_list":["post-641","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11th-physics","category-class-xith","category-jee","tag-downstream-upstream-swimming","tag-drift","tag-motion-of-man-while-crossing-a-river","tag-relative-motion-in-river-flow"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":12,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/641\/revisions"}],"predecessor-version":[{"id":1600,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/641\/revisions\/1600"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media\/1127"}],"wp:attachment":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media?parent=641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/categories?post=641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/tags?post=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}