{"id":2991,"date":"2022-12-17T09:52:19","date_gmt":"2022-12-17T14:52:19","guid":{"rendered":"https:\/\/josmfs.net\/?p=2991"},"modified":"2024-04-06T09:33:58","modified_gmt":"2024-04-06T13:33:58","slug":"fireworks-rocket","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/12\/17\/fireworks-rocket\/","title":{"rendered":"Fireworks Rocket"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2989\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/12\/Fireworks-Rocket-Fig2.jpg\" alt=\"\" width=\"152\" height=\"303\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/12\/Fireworks-Rocket-Fig2.jpg 302w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/12\/Fireworks-Rocket-Fig2-150x300.jpg 150w\" sizes=\"auto, (max-width: 152px) 100vw, 152px\" \/>This is another physics-based problem from Colin Hughes\u2019s <em>Maths Challenge<\/em> website (mathschallenge.net) that may take a bit more thought.<\/p>\n<p>\u201cA firework rocket is fired vertically upwards with a constant acceleration of 4 m\/s<sup>2<\/sup> until the chemical fuel expires. Its ascent is then slowed by gravity until it reaches a maximum height of 138 metres.<\/p>\n<p>Assuming no air resistance and taking <em>g<\/em> = 9.8 m\/s<sup>2<\/sup>, how long does it take to reach its maximum height?\u201d<\/p>\n<p>I can never remember the formulas relating acceleration, velocity, and distance, so I always derive them via integration.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Fireworks-Rocket-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/12\/Fireworks-Rocket-220618.pdf\">Fireworks Rocket<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another physics-based problem from Colin Hughes\u2019s Maths Challenge website (mathschallenge.net) that may take a bit more thought. \u201cA firework rocket is fired vertically upwards with a constant acceleration of 4 m\/s2 until the chemical fuel expires. Its ascent is then slowed by gravity until it reaches a maximum height of 138 metres. Assuming [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[133,32,151],"class_list":["post-2991","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-algebra","tag-calculus","tag-colin-hughes"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2991","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2991"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2991\/revisions"}],"predecessor-version":[{"id":3578,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2991\/revisions\/3578"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2991"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2991"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2991"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}