{"id":3215,"date":"2013-08-14T00:30:31","date_gmt":"2013-08-14T08:30:31","guid":{"rendered":"http:\/\/bendwavy.org\/wp\/?p=3215"},"modified":"2013-09-22T10:32:44","modified_gmt":"2013-09-22T18:32:44","slug":"high-throw","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=3215","title":{"rendered":"High Throw"},"content":{"rendered":"<p><a href=\"http:\/\/what-if.xkcd.com\/44\/\">Read this first.<\/a><\/p>\n<p>To throw for maximum distance (on an infinite plane in a vacuum), you aim at 45\u00b0 elevation; in other words, split kinetic energy evenly between vertical and lateral velocity.  (I dimly remember having proven that, but am not awake enough to do it again now.)<br \/>\nIt follows that the kinetic energy of a perfect vertical throw is twice the <em>vertical<\/em> kinetic energy of a perfect distance throw.<\/p>\n<p>The arc of the latter is a parabola, of course, and its height is easily found to be a quarter of its length.  Double that, because with double the energy you get double the altitude; and the result is consistent with Munroe&#8217;s estimate.<\/p>\n<p>What about air resistance?  The vertical throw has a moment of zero speed, but the distance throw&#8217;s minimum speed is 1\/&radic;2 the maximum; so it seems to me that the vertical throw suffers less air resistance (not even considering the thinner air up there), and therefore the altitude estimate given above is low.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Read this first. To throw for maximum distance (on an infinite plane in a vacuum), you aim at 45\u00b0 elevation; in other words, split kinetic energy evenly between vertical and lateral velocity. (I dimly remember having proven that, but am &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=3215\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-3215","post","type-post","status-publish","format-standard","hentry","category-sciences"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3215","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3215"}],"version-history":[{"count":2,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3215\/revisions"}],"predecessor-version":[{"id":3245,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3215\/revisions\/3245"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}