{"id":54046,"date":"2025-10-08T04:59:47","date_gmt":"2025-10-07T19:59:47","guid":{"rendered":"https:\/\/phys-edu.net\/wp\/?p=54046"},"modified":"2025-10-08T04:59:47","modified_gmt":"2025-10-07T19:59:47","slug":"physics-in-the-park-finding-the-hidden-math-in-a-water-fountain","status":"publish","type":"post","link":"https:\/\/phys-edu.net\/wp\/?p=54046&lang=en","title":{"rendered":"Physics in the Park: Finding the Hidden Math in a Water Fountain"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #339966;\"><strong>This is Ken Kuwako, the Science Trainer. Every day is an experiment!<\/strong><\/span><\/p>\n<p>A walk in the park might seem ordinary. But if you stop and look at it through the eyes of a scientist, it transforms into a laboratory full of wonder and discovery. Take, for example, the water flowing from a drinking fountain. Would you be surprised to learn that the beautiful arc it creates perfectly hides a bit of math you probably learned in middle school?<\/p>\n<p>Today, let&#8217;s uncover the secret behind this &#8220;mathematical art&#8221; found in the park.<\/p>\n<h3>The Secret Behind the &#8220;Mathematical Art&#8221; in the Park<\/h3>\n<p>First, take a look at this video. It&#8217;s nothing more than a simple water fountain being turned on.<\/p>\n<p><iframe loading=\"lazy\" title=\"\u516c\u5712\u306e\u4e2d\u3067\u898b\u3064\u3051\u305f\u8ca0\u306e\uff12\u6b21\u95a2\u6570\u3010\u79d1\u5b66\u306e\u30cd\u30bf\u5e33\u3011\" width=\"1140\" height=\"641\" src=\"https:\/\/www.youtube.com\/embed\/xqMiQUyoChA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>As the water shoots out, it falls in a perfect arc. When I analyzed the trajectory of this water, I found that it aligns incredibly well with the graph of a negative quadratic function\u2014in other words, a clean parabola.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-34231\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/69fc4b21ddb16579f666390a2d18a8e9.jpg\" alt=\"\" width=\"1136\" height=\"764\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/69fc4b21ddb16579f666390a2d18a8e9.jpg 1136w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/69fc4b21ddb16579f666390a2d18a8e9-300x202.jpg 300w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/69fc4b21ddb16579f666390a2d18a8e9-1024x689.jpg 1024w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/69fc4b21ddb16579f666390a2d18a8e9-768x517.jpg 768w\" sizes=\"auto, (max-width: 1136px) 100vw, 1136px\" \/><\/p>\n<p>It\u2019s almost as if someone traced a graph from a math textbook with an invisible pen!<\/p>\n<h3>Why Does Water Form a Parabola? A Peek into the Laws of Physics<\/h3>\n<p>This beautiful curve isn&#8217;t a coincidence. It\u2019s drawn by the rules that govern everything in the universe: the laws of physics. Here&#8217;s how it works:<\/p>\n<p>Upward Force: Water pushed from the tap has an initial upward momentum (initial velocity).<\/p>\n<p>Constant Gravity: However, as long as it&#8217;s on Earth, the water is constantly being pulled straight down by gravity. This force gradually slows the water&#8217;s upward momentum until it eventually begins to fall.<\/p>\n<p>The combination of this forward momentum and the downward pull of gravity creates the same beautiful parabolic trajectory you see when you throw a ball. &#x26be;<\/p>\n<h3>Not Quite Perfect? Nature&#8217;s Special Ingredient: Surface Tension<\/h3>\n<p>However, nature doesn&#8217;t always follow the textbook perfectly. If you watch the video closely, you&#8217;ll notice moments where the parabola&#8217;s shape breaks down slightly, depending on the water&#8217;s pressure. The culprit? Surface tension.<\/p>\n<p>This is the force that causes water molecules to &#8220;hold hands&#8221; and pull together into the smallest possible shape. This force can cause droplets to merge and grow larger, which changes the air resistance and causes the trajectory to deviate slightly from a perfect curve.<\/p>\n<p>Isn&#8217;t it fascinating to see both a perfect mathematical model and nature&#8217;s own little &#8220;imperfections&#8221; at play in such a simple phenomenon?<\/p>\n<p>Next time you&#8217;re near a park, try to find your own piece of &#8220;mathematical art.&#8221; By the way, if you enjoy discovering interesting curves hidden in everyday life, this DVD is a lot of fun!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-54033 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2025-10-08-4.29.39.jpg\" alt=\"\" width=\"201\" height=\"277\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2025-10-08-4.29.39.jpg 420w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/01\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2025-10-08-4.29.39-218x300.jpg 218w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/><\/p>\n<div style=\"text-align: center;\" data-channelid=\"UCBoF1yPvFnXnSJ_Xe5AmXcw\" data-layout=\"full\" data-count=\"default\"><a href=\"https:\/\/amzn.to\/432QHFJ\">Mathematical Curves Hidden in Daily Life DVD-Book<\/a><\/div>\n<div class=\"g-ytsubscribe\" data-channelid=\"UCBoF1yPvFnXnSJ_Xe5AmXcw\" data-layout=\"full\" data-count=\"default\"><\/div>\n<h3>Contact &amp; Inquiries<\/h3>\n<p>Bringing the wonder of science closer to you! I create easy-to-understand guides for fun science experiments you can do at home. Feel free to explore!<\/p>\n<ul>\n<li>The content from my &#8220;Science Idea Book&#8221; is now a published book! Learn more <a href=\"https:\/\/amzn.to\/42PMCEL\">here<\/a>.<\/li>\n<li>About the author, Ken Kuwako, click <a href=\"https:\/\/phys-edu.net\/wp\/?page_id=37\">here<\/a>.<\/li>\n<li>For inquiries (writing, lectures, workshops, TV consulting, etc.), click <a href=\"https:\/\/phys-edu.net\/wp\/?page_id=188\">here<\/a>.<\/li>\n<\/ul>\n<p><span class=\"s2\">\u30fbFollow me on <a href=\"https:\/\/x.com\/kuwako\">X<\/a> for the latest updates!<\/span><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/user\/kkuwako\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-35048\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/03\/3d9640dad7bc5538e76f92da1966ee19.jpg\" alt=\"\" width=\"30\" height=\"21\" \/><\/a>Check out my experiment videos on the <a href=\"https:\/\/www.youtube.com\/user\/kkuwako?sub_confirmation=1\">Science Idea Channel<\/a>!<\/p>\n<h3>\uff14\u6708\u306e\u30a4\u30c1\u30aa\u30b7\u5b9f\u9a13\uff01<\/h3>\r\n<ul>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?p=46937&amp;\">\u5149\u306e\u9b54\u6cd5CMY\u30a6\u30a9\u30fc\u30bf\u30fc\u30ad\u30e5\u30fc\u30d6<\/a>\uff1a\u5149\u306e\u9b54\u6cd5\u3092\u4f53\u9a13\u305b\u3088\uff01\u6c34\u3092\u6ce8\u3050\u3068\u65b0\u305f\u306a\u7acb\u65b9\u4f53\u304c\u51fa\u73fe\u3059\u308b\u9b54\u6cd5\u306e\u3088\u3046\u306a\u5b9f\u9a13\u3067\u3059\u3002<\/li>\r\n<\/ul>\r\n<img class=\"alignnone wp-image-47312 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c.jpg\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c.jpg 1292w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-272x300.jpg 272w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-928x1024.jpg 928w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-768x848.jpg 768w\" alt=\"\" width=\"267\" height=\"294\" \/>\r\n<h3 style=\"text-align: left;\"><span style=\"font-size: medium;\"><b><strong>\u30c6\u30ec\u30d3\u756a\u7d44\u30fb\u79d1\u5b66\u76e3\u4fee\u7b49\u306e\u304a\u77e5\u3089\u305b<\/strong><\/b><\/span><\/h3>\r\n<ul>\r\n \t<li>4\u67089\u65e5\uff08\u6728\uff09\u300cTHE\u7a81\u7834\u30d5\u30a1\u30a4\u30eb\u300d\uff08\u65e5\u672c\u30c6\u30ec\u30d3 \uff09\u306e\u79d1\u5b66\u76e3\u4fee\u3092\u884c\u3044\u307e\u3057\u305f\u3002\u591c7\u6642\u301c\u3068\u306a\u308a\u307e\u3059\u3002<\/li>\r\n<\/ul>\r\n<h3><span style=\"font-size: medium;\"><b>\u66f8\u7c4d<strong>\u306e\u304a\u77e5\u3089\u305b<\/strong><\/b><\/span><\/h3>\r\n<ul>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?p=61585\">\u30b5\u30af\u30bb\u30b915 \uff14\u6708\u53f7<\/a>\u306b\u3066\u3001\u91ce\u7403\u306e\u79d1\u5b66\u306b\u3064\u3044\u3066\u8a18\u4e8b\u3092\u57f7\u7b46\u3057\u307e\u3057\u305f\uff082026\/3\uff09<\/li>\r\n \t<li>\u300e\u5927\u4eba\u306e\u305f\u3081\u306e\u9ad8\u6821\u7269\u7406\u5fa9\u7fd2\u5e33\u300f\uff08\u8b1b\u8ac7\u793e\uff09\u2026\u4e00\u822c\u5411\u3051\u306b\u65e5\u5e38\u306e\u7269\u7406\u306b\u3064\u3044\u3066\u516c\u5f0f\u3092\u5143\u306b\u7d10\u89e3\u304d\u307e\u3057\u305f\u3002<a href=\"https:\/\/phys-edu.net\/wp\/?p=1827\">\u7279\u8a2d\u30b5\u30a4\u30c8<\/a>\u3067\u306f\u5b9f\u9a13\u3092\u591a\u6570\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<strong>\u203b\u5897\u5237\u304c\u304b\u304b\u308a\uff16\u5237\u3068\u306a\u308a\u307e\u3057\u305f\uff082026\/02\/01\uff09\r\n<img class=\"alignnone wp-image-10940 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0-300x262.jpg\" sizes=\"(max-width: 220px) 100vw, 220px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0-300x262.jpg 300w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0.jpg 311w\" alt=\"\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8 2014-07-05 0.43.51\" width=\"220\" height=\"192\" \/>\r\n<\/strong><\/li>\r\n \t<li>\u300e\u304d\u3081\u308b!\u5171\u901a\u30c6\u30b9\u30c8 \u7269\u7406\u57fa\u790e \u6539\u8a02\u7248\u300f\uff08\u5b66\u7814\uff09\u2026\u3000\u9ad8\u6821\u7269\u7406\u306e\u53c2\u8003\u66f8\u3067\u3059\u3002\u30a4\u30e9\u30b9\u30c8\u3092\u591a\u304f\u3057\u3066\u30a4\u30e1\u30fc\u30b8\u304c\u6301\u3066\u308b\u3088\u3046\u306b\u63cf\u304d\u307e\u3057\u305f\u3002\u6388\u696d\u306b\u3064\u3044\u3066\u3044\u3051\u306a\u3044\u3001\u7269\u7406\u304c\u82e6\u624b\u3001\u305d\u3093\u306a\u751f\u5f92\u306b\u304a\u3059\u3059\u3081\u3067\u3059\u3002<a href=\"https:\/\/phys-edu.net\/wp\/?p=45322\">\u7279\u8a2d\u30b5\u30a4\u30c8<\/a>\u306f\u3053\u3061\u3089\u3002\r\n<img class=\"alignnone wp-image-45718 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c.jpg\" sizes=\"(max-width: 184px) 100vw, 184px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c.jpg 756w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c-300x269.jpg 300w\" alt=\"\" width=\"184\" height=\"165\" \/><\/li>\r\n<\/ul>\r\n<h3><span style=\"font-size: medium;\"><b>\u8b1b\u5e2b\u30fb\u30b7\u30e7\u30fc\u30fb\u7814\u7a76\u7b49\u306e\u304a\u77e5\u3089\u305b<\/b><\/span><\/h3>\r\n<ul>\r\n \t<li>3\/20\uff08\u91d1\uff09\u3000\u65e5\u672c\u7406\u79d1\u6559\u80b2\u5b66\u4f1a\u30aa\u30f3\u30e9\u30a4\u30f3\u5168\u56fd\u5927\u4f1a2026\u300c<a href=\"https:\/\/phys-edu.net\/wp\/?p=60439\">\u6163\u6027\u306e\u6cd5\u5247\u306e\u6982\u5ff5\u5f62\u6210\u3092\u76ee\u6307\u3057\u305f\u63a2\u7a76\u7684\u306a\u5b66\u3073\u306e\u5b9f\u8df5\u300d<\/a>\u306b\u3064\u3044\u3066\u767a\u8868\u3057\u307e\u3057\u305f\u3002<\/li>\r\n \t<li>6\/14\uff08\u65e5\uff09\u3000\u5343\u8449\u5927\u5b66\u30a4\u30f3\u30b9\u30bf\u30ec\u30fc\u30b7\u30e7\u30f3\u300c\u63a2\u7a76\u300d\u306b\u3066\u8b1b\u5e2b\u3092\u52d9\u3081\u307e\u3059<\/li>\r\n \t<li>7\/18\uff08\u571f\uff09\u3000<a href=\"https:\/\/phys-edu.net\/wp\/?p=60018\">\u6559\u54e1\u5411\u3051\u5b9f\u9a13\u8b1b\u7fd2\u4f1a\u300c\u30ca\u30ea\u30ab\u30ab\u30b5\u30a4\u30a8\u30f3\u30b9\u30a2\u30ab\u30c7\u30df\u30fc\u300d\u306e\u8b1b\u5e2b\u3092\u3057\u307e\u3059<\/a>\u3002\u304a\u4f1a\u3044\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\r\n 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href=\"http:\/\/phys-edu.net\/wp\/?page_id=20940\">\u8b1b\u6f14<\/a>\u00a0\u2026\u5168\u56fd\u5404\u5730\u3067\u5b9f\u9a13\u8b1b\u7fd2\u4f1a\u30fb\u30b5\u30a4\u30a8\u30f3\u30b9\u30b7\u30e7\u30fc\u7b49\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002<\/li>\r\n \t<li><a href=\"http:\/\/phys-edu.net\/wp\/?page_id=37\">About<\/a>\u00a0\u2026\u300c\u79d1\u5b66\u306e\u30cd\u30bf\u5e33\u300d\u306e\u30b3\u30f3\u30bb\u30d7\u30c8\u3084\u3001\u904b\u55b6\u8005\u3067\u3042\u308b\u6851\u5b50\u7814\u306e\u30d7\u30ed\u30d5\u30a3\u30fc\u30eb\u30fb\u60f3\u3044\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/li>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?page_id=188\">\u304a\u554f\u3044\u5408\u308f\u305b<\/a>\u00a0\u2026\u5b9f\u9a13\u6559\u5ba4\u306e\u3054\u4f9d\u983c\u3001\u57f7\u7b46\u30fb\u8b1b\u6f14\u306e\u76f8\u8ac7\u3001\u79d1\u5b66\u76e3\u4fee\u7b49\u306f\u3053\u3061\u3089\u306e\u30d5\u30a9\u30fc\u30e0\u304b\u3089\u304a\u5bc4\u305b\u304f\u3060\u3055\u3044\u3002<\/li>\r\n<\/ul>\r\n<ul class=\"wp-block-latest-posts__list is-grid columns-3 has-dates wp-block-latest-posts\"><li><div class=\"wp-block-latest-posts__featured-image\"><a href=\"https:\/\/phys-edu.net\/wp\/?p=62514&#038;lang=es\" aria-label=\"\u00a1Gira, lanza y vuela! 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Learn Chemical Changes with Citric Acid \u00d7 Baking Soda (Endothermic Reaction)","author":"\u6851\u5b50 \u7814","date":"2026\u5e742\u670810\u65e5","format":false,"excerpt":"I am Ken Kuwako, your Science Trainer. 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