{"id":21163,"date":"2026-01-22T08:05:00","date_gmt":"2026-01-22T13:05:00","guid":{"rendered":"https:\/\/blog.espol.edu.ec\/algoritmos101\/?p=21163"},"modified":"2026-02-01T02:35:41","modified_gmt":"2026-02-01T07:35:41","slug":"2eva2025paoii_t2-edo-trayectoria-avion-papel","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva30\/2eva2025paoii_t2-edo-trayectoria-avion-papel\/","title":{"rendered":"2Eva2025PAOII_T2 EDO trayectoria avi\u00f3n de papel"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2da Evaluaci\u00f3n 2025-2026 PAO II. 20\/Enero\/2026<\/h2>\n\n\n\n<p><strong>Tema 2<\/strong> (30 puntos) <\/p>\n\n\n\n<p>Para un planeador de papel se estima la velocidad y \u00e1ngulo de inclinaci\u00f3n en un caso particular con las siguientes expresiones [1]:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{dv}{dt} = -0.1388 v^2 - g \\sin(\\omega)<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{d\\omega}{dt} = \\frac{0.7654 v^2 - g\\cos(\\omega)}{v}<\/span>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{dx}{dt} = v\\cos(\\omega)<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{dy}{dt} = v \\sin(\\omega)<\/span>\n<\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"289\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2026\/01\/avionpapel_planeadorejes.gif\" alt=\"avi\u00f3n papel planeador ejes\" class=\"wp-image-21165\" style=\"object-fit:cover\" \/><\/figure>\n\n\n\n<p>Los valores iniciales para el ejercicio se consideran como:<br>g=9.8 m\/s<sup>2<\/sup>, t<sub>0<\/sub> = 0, v<sub>0<\/sub>=4, \u03c9<sub>0<\/sub> =0,<br>x<sub>0<\/sub>=0, y<sub>0<\/sub>=2<\/p>\n\n\n\n<p>a. Plantear del ejercicio para v(t), \u03c9(t) usando Runge-Kutta de 2do Orden<\/p>\n\n\n\n<p>b. Desarrollar tres iteraciones para v(t), \u03c9(t) con tama\u00f1o de paso h=0.1<\/p>\n\n\n\n<p>c. Aproximar la soluci\u00f3n entre t=0 a t=4, usando el algoritmo y adjunte sus resultados en la evaluaci\u00f3n.<\/p>\n\n\n\n<p>d. Observar los resultados para v(t), \u00bfse puede extender en el tiempo y ser v\u00e1lidas?<\/p>\n\n\n\n<p><strong>R\u00fabrica<\/strong>: literal a (5 puntos), literal b (15 puntos), literal c (5 puntos), literal d (5 puntos)<\/p>\n\n\n\n<p><strong>Referencia<\/strong>: [1] Ecuaciones diferenciales \u2014 trayectoria de un avi\u00f3n de papel. MODE-Lab. 17 marzo 2023. https:\/\/www.youtube.com\/watch?v=DPRUnqaNpP8<\/p>\n\n\n\n<p>[2] Paper Airplane Simulation. Supplement for Flight Dynamics by Robert F. Stengel, https:\/\/stengel.mycpanel.princeton.edu\/PaperPlane.html<\/p>\n\n\n\n<p>[3] gr\u00e1fico de planeador, p\u00e1gina 16. https:\/\/stengel.mycpanel.princeton.edu\/FDLecture1.pdf<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Ecuaciones diferenciales \u2014 trayectoria de un avi\u00f3n de papel\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/DPRUnqaNpP8?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>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>2da Evaluaci\u00f3n 2025-2026 PAO II. 20\/Enero\/2026 Tema 2 (30 puntos) Para un planeador de papel se estima la velocidad y \u00e1ngulo de inclinaci\u00f3n en un caso particular con las siguientes expresiones [1]: Los valores iniciales para el ejercicio se consideran como:g=9.8 m\/s2, t0 = 0, v0=4, \u03c90 =0,x0=0, y0=2 a. Plantear del ejercicio para v(t), [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"wp-custom-template-entrada-mn","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[56],"class_list":["post-21163","post","type-post","status-publish","format-standard","hentry","category-mn-2eva30","tag-edo"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21163","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=21163"}],"version-history":[{"count":8,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21163\/revisions"}],"predecessor-version":[{"id":21292,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21163\/revisions\/21292"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=21163"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=21163"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=21163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}