[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/926#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/926","headline":"WurfParabel -Wikipedia","name":"WurfParabel -Wikipedia","description":"before-content-x4 \u30b9\u30ed\u30fc\u3055\u308c\u305f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u307e\u305f\u306f\u6483\u305f\u308c\u305f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u653e\u7269\u7dda\u306e\u8ecc\u8de1 \u3054\u307f\u306e\u653e\u7269\u7dda \u7a7a\u6c17\u62b5\u6297\u306e\u5f71\u97ff\u3092\u7121\u8996\u3059\u308b\u3068\u304d\u306b\u3001\u8eab\u4f53\u304c\u5747\u8cea\u306a\u91cd\u3044\u7551\u3067\u8a18\u8ff0\u3059\u308b\u8ecc\u8de1\u3067\u3059\u3002 [\u521d\u3081] \u50be\u304f \u30eb\u30fc\u30eb\u306f &#8211; \u5782\u76f4\u304a\u3088\u3073\u6c34\u5e73\u30b9\u30ed\u30fc\u306f\u4f8b\u5916\u7684\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002\u6295\u3052\u653e\u7269\u7dda\u306f\u5e38\u306b\u4e0b\u65b9\u306b\u958b\u3044\u3066\u3044\u307e\u3059\u3002\u8ecc\u8de1\u306e\u6700\u9ad8\u70b9\u306f\u3001\u653e\u7269\u7dda\u306e\u9802\u70b9\u3067\u3059\u3002 after-content-x4 \u5730\u7403\u4e0a\u3067\u306f\u3001\u91cd\u3044\u30d5\u30a3\u30fc\u30eb\u30c9\u306f\u3001\u5c0f\u3055\u306a\u6295\u3052\u5e45\u306e\u307f\u3067\u307b\u307c\u5747\u8cea\u3067\u3059\u3002\u305d\u306e\u5f8c\u3001\u653e\u7269\u7dda\u306e\u5f62\u72b6\u306f\u9069\u5207\u306a\u8fd1\u4f3c\u3067\u3059\u3002\u3088\u308a\u826f\u3044\u8fd1\u4f3c\u3067\u306f\u3001\u4f53\u306f\u6955\u5186\u5f62\u306e\u30b1\u30d7\u30e9\u30fc\u30c8\u30e9\u30c3\u30af\u306b\u5f93\u3044\u307e\u3059\u3002 after-content-x4 \u653e\u7269\u7dda\u306e\u30b9\u30ed\u30fc\u306e\u3044\u304f\u3064\u304b\u306e\u5f0f\u306e\u6982\u8981 \u5f3e\u9053 \u7a7a\u6c17\u62b5\u6297\u306e\u5f71\u97ff\u4e0b\u3067\u7406\u60f3\u7684\u306a\u30b9\u30ed\u30fc\u30d1\u30e9\u30dc\u30ea\u30a2\u304b\u3089\u9038\u8131\u3059\u308b\u66f2\u7dda\u3067\u3059\u3002 [2] \u6295\u3052\u308b\u653e\u7269\u7dda\u306f\u3001\u5f3e\u9053\u8ecc\u9053\u306e\u7406\u60f3\u5316\u3067\u3059\u3002 \u5674\u6c34\u306e\u6c34\u306f\u3001\u6295\u3052\u653e\u7269\u7dda\u306e\u5f62\u3092\u305f\u3069\u308a\u307e\u3059\u3002 \u653e\u7269\u7dda\u306e\u5f62\u306e\u7406\u7531\u306f\u3001\u98db\u884c\u4e2d\u306b\u91cd\u529b\u306e\u307f\u304c\u4f53\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3067\u3059\u3002\u7121\u6599\u306e\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u306e\u305f\u3081\u306b\u3001\u521d\u671f\u901f\u5ea6\u306f\u4e92\u3044\u306b\u5782\u76f4\u306b\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306b\u3042\u308a\u307e\u3059 \u306e","datePublished":"2023-09-21","dateModified":"2023-09-21","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a4\/Parabolic_trajectory.svg\/220px-Parabolic_trajectory.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a4\/Parabolic_trajectory.svg\/220px-Parabolic_trajectory.svg.png","height":"91","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/926","wordCount":13115,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u30b9\u30ed\u30fc\u3055\u308c\u305f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u307e\u305f\u306f\u6483\u305f\u308c\u305f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u653e\u7269\u7dda\u306e\u8ecc\u8de1  \u3054\u307f\u306e\u653e\u7269\u7dda \u7a7a\u6c17\u62b5\u6297\u306e\u5f71\u97ff\u3092\u7121\u8996\u3059\u308b\u3068\u304d\u306b\u3001\u8eab\u4f53\u304c\u5747\u8cea\u306a\u91cd\u3044\u7551\u3067\u8a18\u8ff0\u3059\u308b\u8ecc\u8de1\u3067\u3059\u3002 [\u521d\u3081]  \u50be\u304f \u30eb\u30fc\u30eb\u306f &#8211; \u5782\u76f4\u304a\u3088\u3073\u6c34\u5e73\u30b9\u30ed\u30fc\u306f\u4f8b\u5916\u7684\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002\u6295\u3052\u653e\u7269\u7dda\u306f\u5e38\u306b\u4e0b\u65b9\u306b\u958b\u3044\u3066\u3044\u307e\u3059\u3002\u8ecc\u8de1\u306e\u6700\u9ad8\u70b9\u306f\u3001\u653e\u7269\u7dda\u306e\u9802\u70b9\u3067\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5730\u7403\u4e0a\u3067\u306f\u3001\u91cd\u3044\u30d5\u30a3\u30fc\u30eb\u30c9\u306f\u3001\u5c0f\u3055\u306a\u6295\u3052\u5e45\u306e\u307f\u3067\u307b\u307c\u5747\u8cea\u3067\u3059\u3002\u305d\u306e\u5f8c\u3001\u653e\u7269\u7dda\u306e\u5f62\u72b6\u306f\u9069\u5207\u306a\u8fd1\u4f3c\u3067\u3059\u3002\u3088\u308a\u826f\u3044\u8fd1\u4f3c\u3067\u306f\u3001\u4f53\u306f\u6955\u5186\u5f62\u306e\u30b1\u30d7\u30e9\u30fc\u30c8\u30e9\u30c3\u30af\u306b\u5f93\u3044\u307e\u3059\u3002         (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u653e\u7269\u7dda\u306e\u30b9\u30ed\u30fc\u306e\u3044\u304f\u3064\u304b\u306e\u5f0f\u306e\u6982\u8981  \u5f3e\u9053 \u7a7a\u6c17\u62b5\u6297\u306e\u5f71\u97ff\u4e0b\u3067\u7406\u60f3\u7684\u306a\u30b9\u30ed\u30fc\u30d1\u30e9\u30dc\u30ea\u30a2\u304b\u3089\u9038\u8131\u3059\u308b\u66f2\u7dda\u3067\u3059\u3002 [2] \u6295\u3052\u308b\u653e\u7269\u7dda\u306f\u3001\u5f3e\u9053\u8ecc\u9053\u306e\u7406\u60f3\u5316\u3067\u3059\u3002  \u5674\u6c34\u306e\u6c34\u306f\u3001\u6295\u3052\u653e\u7269\u7dda\u306e\u5f62\u3092\u305f\u3069\u308a\u307e\u3059\u3002 \u653e\u7269\u7dda\u306e\u5f62\u306e\u7406\u7531\u306f\u3001\u98db\u884c\u4e2d\u306b\u91cd\u529b\u306e\u307f\u304c\u4f53\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3067\u3059\u3002\u7121\u6599\u306e\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u306e\u305f\u3081\u306b\u3001\u521d\u671f\u901f\u5ea6\u306f\u4e92\u3044\u306b\u5782\u76f4\u306b\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306b\u3042\u308a\u307e\u3059 \u306e 0x{displaystyle v_ {mathrm {0x}}} \u3068        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u306e 0y{displaystyle v_ {mathrm {0y}}} \u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u5206\u89e3\u3002\u6c34\u5e73 \u30d0\u30c4 {displaystyle x} \u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306f\u3001\u5782\u76f4\u304b\u3089\u5b8c\u5168\u306b\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059 \u3068 {displaystyle y}  &#8211; \u4e0a\u5411\u304d\u306b\u5411\u3051\u3089\u308c\u305f\u4f1d\u7d71\u3002\u3053\u308c\u306b\u306f\u6b21\u306e\u7d50\u679c\u304c\u3042\u308a\u307e\u3059\uff08\u51fa\u767a\u70b9\u3067\u3059 \u30d0\u30c4 = 0 \u3001 \u3068 = 0 {displaystyle x = 0\u3001\u3001y = 0} \uff09\uff1a \u6c34\u5e73\u65b9\u5411\u306b\u306f\u3001\u6700\u521d\u306e\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306e\u5f8c\u3001\u4f53\u306f\u4e00\u5b9a\u306e\u901f\u5ea6\u3067\u98db\u884c\u3057\u307e\u3059 \u306e 0x{displaystyle v_ {mathrm {0x}}} \u3053\u306e\u65b9\u5411\u306b\u5f7c\u306b\u529b\u304c\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u4e00\u5b9a\u306e\u901f\u5ea6\u3067\u306f\u3001\u8ddd\u96e2\u306f\u6642\u9593\u3068\u3068\u3082\u306b\u76f4\u7dda\u7684\u306b\u5909\u5316\u3057\u307e\u3059\u3002\u5f0f\u306f\u3053\u306e\u8ddd\u96e2\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002 x(t)=v0x\u22c5t{displaystyle x\uff08t\uff09= v_ {mathrm {0x}} cdot t} \u5782\u76f4\u65b9\u5411\u3067\u306f\u3001\u91cd\u529b\u306f\u4e00\u5b9a\u306e\u52a0\u901f\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u91cd\u5ea6\u306e\u52a0\u901f\u5ea6\u304c\u767a\u751f\u3057\u307e\u3059 g = 9 ,81 ms2{displaystyle Text Style G = 9 {\u3001} 81\u3001{frac {mathrm {m}} {mathrm {s} ^{2}}}} \u3002\u901f\u5ea6\u7528 \u306e y{displaystyle v_ {mathrm {y}}} \u8a72\u5f53\u3059\u308b\uff1a vy(t)=v0y\u2212g\u22c5t{displaystyle v_ {mathrm {y}}\uff08t\uff09= v_ {mathrm {0y}} -gcdot t} \u5834\u6240 \u3068 {displaystyle y} \u3053\u308c\u306f\u3001\u6642\u9593\u306e\u7d4c\u904e\u306b\u4f34\u3046\u7d71\u5408\u3092\u901a\u3058\u3066\u3053\u308c\u306b\u8d77\u56e0\u3057\u307e\u3059\u3002 y(t)=v0y\u22c5t\u2212g2\u22c5t2{displaystyle y\uff08t\uff09= v_ {mathrm {0y}} cdot t- {frac {g} {2}} cdot t^{2}} \uff08\u2192\u81ea\u7531\u30b1\u30fc\u30b9\u306e\u4e00\u822c\u5f0f\uff09 Table of Contents\u6570\u5b66\u7684\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7bc4\u56f2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u5927\u7bc4\u56f2\u306e\u958b\u59cb\u89d2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u521d\u671f\u9ad8\u3055\u306e\u6700\u5927\u7bc4\u56f2 h 0 \u22600 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e0a\u90e8\u304a\u3088\u3073\u4e0b\u89d2\u5ea6\u30b0\u30eb\u30fc\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30bc\u30ed\u306e\u7570\u306a\u308b\u521d\u671f\u9ad8\u3055\u306e\u7bc4\u56f2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b9\u30dd\u30c3\u30c8 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5ea7\u6a19 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3059\u3079\u3066\u306e\u5782\u76f4\u70b9\u306e\u5c40\u6240\u66f2\u7dda [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f8b\u306e\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5782\u76f4\u30b9\u30ed\u30fc [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6c34\u5e73\u30ea\u30c3\u30bf\u30fc [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6295\u3052\u653e\u30ef\u3092\u5305\u307f\u307e\u3059 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u52fe\u914d\u4e0a\u306e\u5c0f\u7269\u306e\u30ef\u30fc\u30d5\u5e45 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6570\u5b66\u7684\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f53\u306f\u901f\u5ea6\u3067\u3059 \u306e 0 {displaystyle v_ {0}} \u89d2\u5ea6\u306e\u4e0b b {displaystyle\u30d9\u30fc\u30bf} \u4e0a\u5411\u304d\u306b\u6295\u3052\u3089\u308c\u307e\u3059\u3002\u6b21\u306b\u3001\u30c9\u30ed\u30c3\u30d7\u306e\u4f4e\u4e0b\u304c\u7dda\u5f62\u306e\u91cd\u306d\u5408\u308f\u305b\u306b\u3088\u3063\u3066\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u901f\u5ea6\u6210\u5206\u306b\u9069\u7528\u3055\u308c\u307e\u3059\uff08\u7a7a\u6c17\u62b5\u6297\u3092\u7121\u8996\u3057\u307e\u3059\uff09\u3002 \u6c34\u5e73\uff1a \u306e 0x= \u306e 0cos \u2061 b {displaystyle v_ {mathrm {0x}} = v_ {0} cos beta} \u5782\u76f4\uff1a \u306e 0y= \u306e 0\u7f6a \u2061 b {displaystyle v_ {mathrm {0y}} = v_ {0} sin beta} \u3053\u308c\u306f\u6b21\u306e\u7d50\u679c\u3067\u3059 \u30d0\u30c4 {displaystyle x} &#8211; \u3068 \u3068 {displaystyle y} -ART\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u4ee5\u4e0b\uff1a \u6c34\u5e73\uff1a\u521d\u671f\u901f\u5ea6\u306e\u6c34\u5e73\u6210\u5206\uff1a x(t)=v0tcos\u2061\u03b2(1){displaystyle x\uff08t\uff09= v_ {0} tcos beta qquad\uff081\uff09} \u3068 \u5782\u76f4\uff1a\u521d\u671f\u901f\u5ea6\u306e\u5782\u76f4\u6210\u5206\u3068\u4e00\u5b9a\u306e\u52a0\u901f\u306b\u3088\u308b\u901f\u5ea6\u5909\u5316\uff1a y(t)=v0tsin\u2061\u03b2\u2212g2t2(2){displaystyle y\uff08t\uff09= v_ {0} tsin beta- {frac {g} {2}} t^{2} qquad\uff082\uff09} \u30d9\u30af\u30c8\u30eb\u9244\u9053\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 r\u2192\uff08 t \uff09\uff09 = (x(t)y(t))= (v0tcos\u2061\u03b2v0tsin\u2061\u03b2\u2212g2t2){displaystyle {vec {r}}\uff08t\uff09= {begin {pmatrix} x\uff08t\uff09\\ y\uff08t\uff09end {pmatrix}}} = {begin {pmatrix} v_ {0} tcos beta \\ v_ {0}} tsin beta- {g {{{2 {{{2} {{{{2 {{{{{2 {{{{{2 {{{{{{{{{{{2 {{{2 {{{{{{2 {{{2 {{{{2 {{{{{{{{{{{{2}\uff09 }}} \u753a\u306e\u5730\u57df\u306e\u660e\u793a\u7684\u306a\u9244\u9053\u65b9\u7a0b\u5f0f\uff081\u3064\u3067 \uff08 \u521d\u3081 \uff09\uff09 {displaystyle\uff081\uff09} \u5f8c t {displaystylet} \u89e3\u6c7a\u3057\u3066\u304b\u3089 t {displaystylet} \u306e \uff08 2 \uff09\uff09 {displaystyle\uff082\uff09} \u633f\u5165\uff09\u8aad\u307f\u53d6\u308a\uff1a \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 = \u30d0\u30c4 \u89e3\u6c7a\u3057\u307e\u3059 \u2061 b  &#8211;  g2v02cos2\u2061\u03b2\u30d0\u30c4 2{displaystyle y\uff08x\uff09= xtan beta- {frac {g} {2 {v_ {0}}^{2} cos^} beta}}} x^{2}}}}}}}} \u7bc4\u56f2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7bc4\u56f2 r {displaystyle r} \u901a\u5e38\u3001\u3054\u307f\u306e\u653e\u7269\u7dda\u304c\u518d\u3073\u51fa\u529b\u306e\u9ad8\u3055\u306b\u9054\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 H\u3002\uff1a \u3068 \uff08 r \uff09\uff09 = 0 {displaystyle y\uff08r\uff09= 0} \u3002\u3053\u308c\u306f\u3001\u52d5\u304d\u306e\u65b9\u7a0b\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059 r {displaystyle r} \u6eb6\u304b\u3057\u3066\u53d6\u5f97\uff1a r = v02g\u7f6a \u2061 \uff08 2 b \uff09\uff09 {displaystyle r = {frac {{v_ {0}}^{2}} {g}} sin\uff082beta\uff09} \u6700\u5927\u7bc4\u56f2\u306e\u958b\u59cb\u89d2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u526f\u9f3b\u8154\u306f\u6a5f\u80fd\u3057\u3066\u3044\u307e\u3059 90 \u2218 {displaystyle 90^{circ}} \u5f7c\u3089\u306e\u6700\u5927\u306e\u4fa1\u5024 \u7f6a \u2061 90 \u2218 = \u521d\u3081 {displaystyle sin 90^{circ} = 1} \u6301\u3063\u3066\u3044\u308b\u3001\u3042\u306a\u305f\u306f\u521d\u671f\u984d\u3067\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 h 0 = 0 {displaystyle h_ {0} = 0} \u306e\u6700\u5927\u306e\u7bc4\u56f2 b max= 45 \u2218 {displaystyle beta _ {mathrm {max}} = 45^{circ}} \u3002 \u521d\u671f\u9ad8\u3055\u306e\u6700\u5927\u7bc4\u56f2 h 0 \u22600 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] b max= \u30a2\u30fc\u30af\u30b7\u30f3 \u2061 v02v02+2gh0= Arccos \u2061 v02+2gh02v02+2gh0= arccot \u2061 1+2gh0v02{displaystyle beta _ {mathrm {max}} = arcsin {frac {v_ {0}} {sqrt {2 {v_ {0}}^{2}+2gh_ {0}}}}} = arccos {sqrt {{{{{{{{v_} {{v_} {{v_} 0}} {2 {v_ {0}}^{2}+2gh_ {0}}}} = operatorname {arccot}} {sqrt {1+ {frac {2gh_ {0}} {{v_ {0}}^{2}}}}}} Arkuskosinus\u306e\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u306f\u3001Arcussinus\u306e\u8868\u73fe\u306b\u8d77\u56e0\u3057\u3001\u6700\u7d42\u8868\u73fe\u306e\u5834\u5408\u30012\u3064\u306e\u4ee5\u524d\u306e\u5f0f\u306e\u8b70\u8ad6\u306f\u4e92\u3044\u306b\u5171\u6709\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u521d\u671f\u306e\u9ad8\u3055\u306f\u76ee\u7684\u5730\u306e\u4e0b\u306b\u3042\u308b\u3060\u3051\u306a\u306e\u3067\u3001\u30b9\u30ed\u30fc\u8ddd\u96e2\u306e\u5782\u76f4\u6295\u3052\u3067\u3053\u308c\u3092 0 {displaystyle 0} \u305f\u3060\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3001 h 0\u2265  &#8211;  v022g{displaystyle h_ {0} geq -{frac {{v_ {0}}^{2}} {2g}}}} \u30c9\u30ed\u30c3\u30d7\u306e\u9ad8\u3055\u304b\u3089\u306e\u3082\u306e h 0 {displaystyle h_ {0}} \u5f93\u5c5e\u6700\u5927\u6c34\u5e73\u30b9\u30ed\u30fc\u8ddd\u96e2\u306f\u3067\u3059 r max\uff08 \u306e 0 \u3001 h 0 \uff09\uff09 = v0g v02+ 2 g h0{displaystyle r_ {mathrm {max}}\uff08v_ {0}\u3001h_ {0}\uff09= {frac {v_ {0}} {g}} {sqrt {{v_ {0}}}^{2}+2GH_ {0}}}}}}}}}}} \u306e\u98db\u884c\u6642\u9593\u4ed8\u304d \u521d\u3081 g 2 v02+ 2 g h0{displaystyle {frac {1} {g}} {sqrt {2 {v_ {0}}^{2}+2gh_ {0}}}}} \u3002 \u6700\u5927\u30b9\u30ed\u30fc\u7bc4\u56f2\u306e\u5f0f\u306f\u3001\u65b9\u7a0b\u5f0f\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6307\u5b9a\u3055\u308c\u305f\u6392\u51fa\u9ad8\u3055\u3068\u30b9\u30ed\u30fc\u7bc4\u56f2\u306e\u6700\u5c0f\u6db2\u901f\u5ea6\u3092\u3082\u305f\u3089\u3057\u307e\u3059 \u306e 0 \uff08 r \u3001 h 0 \uff09\uff09 = g R2+h02 &#8211;  g h0{displaystyle v_ {0}\uff08r\u3001h_ {0}\uff09= {sqrt {g {sqrt {r^{2}+{h_ {0}}^{2}}}  &#8211;  gh_ {0}}}}}}}} \u6700\u9069\u306a\u30c9\u30ed\u30c3\u30d7\u89d2\u3082\u540c\u69d8\u3067\u3059 b \uff08 r \u3001 h 0 \uff09\uff09 = \u30a2\u30fc\u30af\u30b7\u30f3 \u2061 12 &#8211;  h02R2+h02{displaystyle beta\uff08r\u3001h_ {0}\uff09= arcsin {sqrt {{frac {1} {2}}  &#8211;  {frac {h_ {0}} {2 {sqrt {r^{2}+{h_ {0}}^{2}}}}}}}}}}}}}}}}}}}}}}} \u306e\u98db\u884c\u6642\u9593 2gR2+h02{displaystyle {sqrt {{frac {2} {g}} {sqrt {r^{2}+{h_ {0}}^{2}}}}}}}}}}}}}} \u3002 \u305f\u3081\u306b h 0 = 0 {displaystyle h_ {0} = 0} \u3059\u3067\u306b\u65e2\u77e5\u306e\u5f0f\u304c\u767a\u751f\u3057\u307e\u3059\u3002 \u4e0a\u90e8\u304a\u3088\u3073\u4e0b\u89d2\u5ea6\u30b0\u30eb\u30fc\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e0a\u90e8\uff08\u9752\u300171.1\u00b0\uff09\u304a\u3088\u3073\u4e0b\uff08\u30aa\u30ec\u30f3\u30b8\u300118.9\u00b0\uff09\u89d2\u7fa4\u306e\u4f8b\u3002\u3069\u3061\u3089\u3082\u3001\u305f\u3068\u3048\u8a71\u3092\u6295\u3052\u308b\u306e\u306f\u3001\u540c\u3058\u521d\u671f\u901f\u5ea6\u3067100 m\u306e\u8ddd\u96e2\u3067\u30b4\u30fc\u30eb\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 \u3054\u307f\u306f\u3001\u7279\u5b9a\u306e\u8ddd\u96e2\u3067\u540c\u3058\u9ad8\u3055\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059 r T{displaystyle r_ {mathrm {t}}} \u9054\u6210\u3059\u308b\u305f\u3081\u306b\u3001\u521d\u671f\u901f\u5ea6\u306b\u5fdc\u3058\u3066\u3001\u521d\u671f\u901f\u5ea6\u306b\u5fdc\u3058\u3066\u3001\u307e\u305f\u306f2\u3064\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u521d\u306e\u30b1\u30fc\u30b9\u306f\u3001\u6700\u5927\u7bc4\u56f2\u304c\u76ee\u6a19\u307e\u3067\u306e\u8ddd\u96e2\u3088\u308a\u3082\u4f4e\u3044\u5834\u5408\u306b\u767a\u751f\u3057\u307e\u3059\u3002 2\u756a\u76ee\u306e\u30b1\u30fc\u30b9\u306f\u300145\u00b0\u306e\u30b9\u30ed\u30fc\u306b\u3088\u3063\u3066\u76ee\u6a19\u306b\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u5834\u5408\u3002\u3055\u3089\u306b\u9ad8\u3044\u521d\u671f\u901f\u5ea6\u3067\u306f\u3001\u5e38\u306b2\u3064\u306e\u89d2\u5ea6\u304c\u3042\u308a\u3001\u6295\u3052\u653e\u7269\u7dda\u304c\u4e21\u65b9\u306e\u6642\u9593\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u65b9\u7a0b\u5f0f\u306e2\u3064\u306e\u6b63\u306e\u89d2\u5ea6\u3067\u3059 \u7f6a \u2061 \uff08 b \uff09\uff09 cos \u2061 \uff08 b \uff09\uff09 = g2v02r T{displaystyle sin\uff08beta\uff09cos\uff08beta\uff09= {frac {g} {2v_ {0}^{2}}} r_ {mathrm {t}}} \u6e80\u305f\u3059\u3002\u6b63\u78ba\u306a1\u3064\u306e\u6eb6\u6db2\u306f\u5e38\u306b45\u00b0\u3088\u308a\u5927\u304d\u304f\u3001\u3082\u30461\u3064\u306f45\u00b0\u3088\u308a\u3082\u5c0f\u3055\u3044\u3067\u3059\u3002 \u3057\u305f\u304c\u3063\u3066\u300145\u00b0\u3092\u8d85\u3048\u308b\u89d2\u5ea6\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f \u4e0a\u89d2\u30b0\u30eb\u30fc\u30d7 \u4ed6\u306e\u4eba\u3068\u547c\u3070\u308c\u307e\u3059 \u4f4e\u3044\u89d2\u5ea6\u30b0\u30eb\u30fc\u30d7\u3002 \u7832\u5175\u306e\u8aad\u307f\u7269\u3067\u306f\u3001\u8feb\u6483\u7832\u307e\u305f\u306f\u5927\u7832\u3067\u306e\u5e73\u3089\u306a\u706b\u3067\u3001\u307e\u305f\u306f\u5927\u6df7\u4e71\u306e\u3042\u308b\u3069\u3061\u3089\u304b\u3067\u6025\u306a\u706b\u3092\u3064\u3051\u3066\u3044\u307e\u3059\u3002 \u4f8b  \u540c\u3058\u9ad8\u3055\u3067100 m\u96e2\u308c\u305f\u30bf\u30fc\u30b2\u30c3\u30c8\u3078\u306e\u30b9\u30ed\u30fc\uff08\u307e\u305f\u306f\u30b7\u30e7\u30c3\u30c8\uff09\u306e\u5834\u5408\u3001\u521d\u671f\u901f\u5ea6\u306f\u901a\u5e38\u306e\u7406\u60f3\u7684\u306a\u4eee\u5b9a\u306e\u4e0b\u306b\u3042\u308a\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\uff08\u6469\u64e6\u306a\u3057\u30019.81 m\/s\u306e\u91cd\u5ea6\u306e\u52a0\u901f 2 \uff09\u5c11\u306a\u304f\u3068\u308231 m\/s\u3067\u3059\u3002\u521d\u671f\u901f\u5ea6\u3067\u3053\u306e\u5024\u3092\u4f7f\u7528\u3059\u308b\u3068\u300145\u00b0\u306e\u30b9\u30ed\u30fc\u306b\u3088\u3063\u3066\u3001\u305d\u308c\u306b\u3088\u3063\u3066\u306e\u307f\u5230\u9054\u3067\u304d\u307e\u3059\u3002\u9ad8\u901f\u5024\u3054\u3068\u306b\u5e38\u306b2\u3064\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u300140 m\/s\u306e\u521d\u671f\u901f\u5ea6\u3067\u306f\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u306f18.9\u00b0\u306e\u89d2\u5ea6\u306771.1\u00b0\u306e\u89d2\u5ea6\u3067\u9054\u6210\u3067\u304d\u307e\u3059\u3002\u98db\u884c\u6642\u9593\u306f\u3001\u4f4e\u3044\u89d2\u5ea6\u30b0\u30eb\u30fc\u30d7\u306e\u6eb6\u6db2\u3067\u306f\u77ed\u304f\u306a\u308a\u307e\u3059\u3002\u4f8b\u3067\u306f\u30012\u756a\u76ee\u306e\u6eb6\u6db2\u306e7.7\u79d2\u3068\u6bd4\u8f03\u3057\u3066\u7d042.6\u79d2\u3067\u3059\u3002 \u30bc\u30ed\u306e\u7570\u306a\u308b\u521d\u671f\u9ad8\u3055\u306e\u7bc4\u56f2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u305f\u3081\u306b b \u2260 0 {displaystyle beta neq 0} \u4e00\u822c\u5f0f\u304c\u9069\u7528\u3055\u308c\u307e\u3059 r = v022g\u7f6a \u2061 \uff08 2 b \uff09\uff09 [ 1+(1+2gh0v02sin2\u2061\u03b2)1\/2] = v0cos\u2061\u03b2g\uff08 v0sin\u2061\u03b2+(v0sin\u2061\u03b2)2+2gh0\uff09\uff09 {displaystyle r = {frac {{v_ {0}}^{2}} {2g}} sin\uff082beta\uff09\u5de6[1+\u5de6\uff081+ {2gh_ {0}} {{v_ {0}}^{2} {2} {2} {2} sin^{2} sin^{2} sin^{2} sin^{2} v_ {0} cos beta} {g}}\u5de6\uff08v_ {0} sin beta +{sqrt {\uff08v_ {0} sin beta\uff09^{2} +2gh_ {0}}}}}}} \u30b9\u30ed\u30fc\u8ddd\u96e2\u306e\u5834\u5408 r {displaystyle r} \u3002\u6700\u5927\u7bc4\u56f2\u3068\u95a2\u9023\u3059\u308b\u958b\u59cb\u89d2\u306f\u3001\u6d3e\u751f\u3092\u4f7f\u7528\u3057\u306a\u304f\u3066\u3082\u3001\u5305\u307f\u8fbc\u3080\u6295\u3052\u653e\u7269\u7dda\u304b\u3089\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002\u305f\u3081\u306b 0}&#8221;>\u306f b max< 45 \u2218 {displaystyle beta _ {mathrm {max}} "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/926#breadcrumbitem","name":"WurfParabel -Wikipedia"}}]}]