{"id":82,"date":"2013-04-30T10:34:41","date_gmt":"2013-04-30T09:34:41","guid":{"rendered":"http:\/\/www.venco.com.pl\/~cozy\/blog\/?p=82"},"modified":"2013-04-30T10:34:41","modified_gmt":"2013-04-30T09:34:41","slug":"zagadka-matematyczno-fizyczna","status":"publish","type":"post","link":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/2013\/04\/30\/zagadka-matematyczno-fizyczna\/","title":{"rendered":"Zagadka matematyczno-fizyczna"},"content":{"rendered":"\n\n<\/col>\n<\/col>\n<\/col>\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Z punktu wyznaczonego przez wsp\u00f3\u0142rz\u0119dne cache’a rusza obiekt kursem 242.45\u00b0 (to jest azymut). Liczba cyfr po przecinku mo\u017ce wywo\u0142a\u0107 emocje, bo dost\u0119pnymi busolami takiego namiaru raczej si\u0119 nie z\u0142apie, ale stosuj\u0105c inne narz\u0119dzia mo\u017cna tak\u0105 z tak\u0105 dok\u0142adno\u015bci\u0105 si\u0119 spotka\u0107. Mimo to nie s\u0105dz\u0119, \u017ceby a\u017c taka dok\u0142adno\u015b\u0107 by\u0142a potrzebna, a nawet wiem to na pewno, \u017ce nie \"Perskie.<\/p>\n

\u00d3w obiekt porusza si\u0119 dosy\u0107 niespokojnie, a jego przyspieszenie jest opisane zale\u017cno\u015bci\u0105:<\/p>\n

a(t)=A*t^3+B*t^2+C*t+D
\ngdzie:
\nA= 2.2407391692082E-8\u00a0\u00a0\u00a0\u00a0 \u00a0[m\/s^5]
\nB= -1.27600374342122E-5\u00a0\u00a0 [m\/s^4]
\nC= 1.45199898164691E-3\u00a0\u00a0\u00a0 [m\/s^3]<\/p>\n

jednocze\u015bnie: a(0)=0 i v(0)=0\u00a0 (v – pr\u0119dko\u015b\u0107)<\/p>\n

Czas ruchu obiektu jest r\u00f3wny T=500s<\/p>\n

Po czasie T obiekt znajduje si\u0119 wi\u0119c przy cache’u<\/p>\n

dane rownanie ma warunki poczatkowe z ktorych mozna obliczyc D.<\/td>\n<\/tr>\n

a nastepnie wzor podwojnie zcalkowa\u0107.<\/td>\n<\/td>\n<\/tr>\n
jesli a(0) = 0 i V(0)=0 wiec D=0<\/td>\n<\/td>\n<\/tr>\n
(bo a(0)=A*0 + B*0 + C*0 + D = 0).<\/td>\n<\/td>\n<\/tr>\n
O ile dobrze pamietam rachunek calkowy to:<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
v=1\/4*A*t^4+1\/3*B*t^3+1\/2*Ct^2+ Dt + V0<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
ale z racji ze D=0 i V0=0 to wzor na predkosc wyglada:<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
v=1\/4*A*t^4+1\/3*B*t^3+1\/2*Ct^2<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
natomiast wzor na droge:<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
s=1\/5*1\/4*A*t^5+1\/4*1\/3*B*t^4+1\/3*1\/2*C*t^3+ s0<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
jesli nie ma drogi poczatkowej to:<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
s=1\/5*1\/4*A*t^5+1\/4*1\/3*B*t^4+1\/3*1\/2*C*t^3<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
A<\/td>\n <\/span>0.0000000224074 <\/span><\/td>\n<\/td>\n<\/tr>\n
B<\/td>\n– <\/span>0.0000127600374 <\/span><\/td>\n<\/td>\n<\/tr>\n
C<\/td>\n <\/span>0.0014519989816 <\/span><\/td>\n<\/td>\n<\/tr>\n
V0<\/td>\n0<\/td>\n<\/td>\n<\/tr>\n
a0<\/td>\n0<\/td>\n<\/td>\n<\/tr>\n
t<\/td>\n500.00<\/td>\n<\/td>\n<\/tr>\n
t^5<\/td>\n31 250 000 000 000.00<\/td>\n <\/span>35 011.55 <\/span><\/td>\n<\/tr>\n
t^4<\/td>\n62 500 000 000.00<\/td>\n– <\/span>66 458.53 <\/span><\/td>\n<\/tr>\n
t^3<\/td>\n125 000 000.00<\/td>\n <\/span>30 249.98 <\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n– <\/span>1 197.00 <\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
s<\/td>\n-1197<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Z punktu wyznaczonego przez wsp\u00f3\u0142rz\u0119dne cache’a rusza obiekt kursem 242.45\u00b0 (to jest azymut). Liczba cyfr po przecinku mo\u017ce wywo\u0142a\u0107 emocje, bo dost\u0119pnymi busolami takiego namiaru raczej si\u0119 nie z\u0142apie, ale stosuj\u0105c inne narz\u0119dzia mo\u017cna tak\u0105 z tak\u0105 dok\u0142adno\u015bci\u0105 si\u0119 spotka\u0107. Mimo to nie s\u0105dz\u0119, \u017ceby a\u017c taka dok\u0142adno\u015b\u0107 by\u0142a potrzebna, a nawet wiem to na…<\/p>\n

Read more →<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[9],"class_list":["post-82","post","type-post","status-publish","format-standard","hentry","category-bez-kategorii","tag-rozne"],"_links":{"self":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts\/82","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/comments?post=82"}],"version-history":[{"count":0,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts\/82\/revisions"}],"wp:attachment":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/media?parent=82"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/categories?post=82"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/tags?post=82"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}