{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":58778,"title":"Count collisions in an idealized block system","description":"Two blocks, which have masses  and , slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed . All of the collisions are elastic. \r\nWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 358.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.35px; transform-origin: 407px 179.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.525px 8px; transform-origin: 101.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTwo blocks, which have masses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.058px 8px; transform-origin: 231.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. All of the collisions are elastic. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.725px 8px; transform-origin: 371.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 203.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 101.85px; text-align: left; transform-origin: 384px 101.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 328px;height: 198px\" 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data-image-state=\"image-loaded\" width=\"328\" height=\"198\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = countCollisions(m1,m2,v1)\r\n  y = length(ode45('NewtonII',tspan,y0));\r\n  ","test_suite":"%%\r\nm1 = 1;\r\nm2 = 1;\r\nv1 = 1;\r\ny_correct = 3;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 2;\r\nm2 = 1;\r\nv1 = 1;\r\ny_correct = 5;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 17;\r\nm2 = 4;\r\nv1 = 8;\r\ny_correct = 6;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 15;\r\nm2 = 1.5;\r\nv1 = 0.3;\r\ny_correct = 10;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 3;\r\nm2 = 0.03;\r\nv1 = 0.5;\r\ny_correct = 31;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 4500000;\r\nm2 = 4.5;\r\nv1 = 0.55;\r\ny_correct = 3141;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 1.8e11;\r\nm2 = 18;\r\nv1 = 5.2;\r\ny_correct = 314159;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np2 = regexprep('11.0010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000','\\.','');\r\nfor k = 2:10\r\n    m2 = rand;\r\n    m1 = 4^k*m2;\r\n    v1 = rand;\r\n    y = countCollisions(m1,m2,v1);\r\n    assert(isequal(dec2bin(y),p2(1:k+2)))\r\nend\r\n\r\n%%\r\np7 = regexprep('3.0663651432036134110263402244652226643520650240155443215426431025161154565220002622436103301443233631','\\.','');\r\nfor k = 2:8\r\n    m2 = rand;\r\n    m1 = 49^k*m2;\r\n    v1 = rand;\r\n    y = countCollisions(m1,m2,v1);\r\n    assert(isequal(dec2base(y,7),p7(1:k+1)))\r\nend\r\n\r\n%%\r\nfiletext = fileread('countCollisions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'classdef'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":46909,"edited_by":46909,"edited_at":"2023-07-22T01:52:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-22T01:47:49.000Z","updated_at":"2023-07-22T01:52:49.000Z","published_at":"2023-07-22T01:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo blocks, which have masses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. All of the collisions are elastic. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"198\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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collisions in an idealized block system","description":"Two blocks, which have masses  and , slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed . All of the collisions are elastic. \r\nWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 358.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.35px; transform-origin: 407px 179.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.525px 8px; transform-origin: 101.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTwo blocks, which have masses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.058px 8px; transform-origin: 231.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAoCAYAAAACJPERAAABiklEQVRYR+2VvS4GQRiFv+8S/FSi4gKIEA2Fwl9UOnrxdwEkRIkgWuIOkEhEoVVQCBqVBndA3AHPSWZlMpnZ3eyOfJHMJieTmdn3nHnP+85us9GCp9kCzUYS/VPXk73J3igOpEaKYmOIpMjeEQJfwIdD0MO8K7BXeGBXtI+ISbAIek30KOOdw/TJvA0cgy3PoXKFQ5kqkzcTuc6477AcMV8xa52xRMX3CAbBGZjzHF37eoYK/XReyKvpNu9ugCcw5cnmlbUDcBJTdA2yvYCFarAr0B4Q7GC9Gzz79vMyFfGtCep3CGTtITj1kC6xtgvUZJt1RGcIvjYEcmAAuHXWIafBBFAv7FQRtTs4E9WVugDDwL27WVJZWSqJiuTbMC0z3oMbMBaqleWEeqG2qOqjq7FQICjdaJmKzK6rrz+i2zsPo69TfeK1M9UH4ryEpbZ4bdE8G0N7SfTXmaKf+L+xN/vX6m6v+k4dM1N9NsfBrBH6YrwED+DdFo8pWroUSbS0VVVeTPZWca10zA8P708pRoZlvQAAAABJRU5ErkJggg==\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. All of the collisions are elastic. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.725px 8px; transform-origin: 371.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 203.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 101.85px; text-align: left; transform-origin: 384px 101.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 328px;height: 198px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAApAAAAGLCAYAAABwTKKVAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAABCUSURBVHhe7d0PrF7lQcfx53UKnbBBbxYccbDeki2pxNAFWzJUKGnGWNwYFTcawRnJKCVhM3RqO4cxMyitukyEpfwxM7JggYk2G1NgFsqYU4ZKq5nVGSlzZiOE3FIHW1udtc/hvO3tn1vu7/7p+6efT3LyPue8B7jNbV6+ec57ntPZu08BAIBJ+oH2FQAAJkVAAgAQEZAAAEQEJAAAEQEJAEBEQAIAEBGQAABEBCQAABEBCQBAREACABARkAAARAQkAAARAQkAQERAAgAQEZAAAEQEJAAAEQEJAEBEQAIAEBGQAABEBCQAABEBCQBAREACABDp7N2nHc+4TqfTjmbGLP6oAABMkhlIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACKdvfu04xnX6XTa0cyYxR8VgNbo6Gh59tln2z3oH/PmzSvbt29v9+glAQnAQepn96ZtY+0e9I+lC0a0QJ9wCRsAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEiCwdu3aZtuyZUt75MhefPHF/efWMcAw6ezdpx3PuE6n045mxiz+qACTMjIyUnbs2FHmzp1bxsbG2qOHu/3228t1113XjJ9++umycOHCZjwI6mf3pm0T/9mgV5YuGNECfcIMJEDgiiuuaF5rRG7evLkZH8kdd9zRvNbQHKR4BJgMAQkQuPbaa9tRKffdd187Oli9ZN29xN0NToBhIiABAnU2sc4qVhMF5L333tuOBCQwnAQkQKg7CznRZexuWNbQXLJkSTMGGCYCEiC0YsWKdnT4LGS9fN2NyvGXuwGGiYAECI2Oju6/MebQgBx/+Xp8aAIMEwEJMAUT3Y3dvfu6BmYNTYBhJCABpmDlypXtqJRbbrmleR1/9/XRLl9v3769WWuxbhYZBwaRgASYglNPPXX/ZezHH3+8eV23bl3zWi1fvrwdHawuMD5//vx2D2AwCUiAKVq9enXz2r2M/dBDDzX79c7rGpiHqk+mqduaNWvKZZdd1h4FGDwCEmCKLrnkknZUyg033PCql6/rDTcbNmwoN998c3sEYDAJSIApqrOM3ZnEbjxWE12+rs/Onug9gEEiIAGm4dAnzYy/ueZo6s0z3SfaAAyazt592vGMq3cYzqRZ/FEBpmzt2rXN686dO5u1HyezfM+yZcvKxo0bm+9PHun7kr1UP7s3bRtr96B/LF0wogX6hIAE6IGLLrqobN26tTzzzDMCEiZJQPYPl7ABeqBGY519BBhEAhKgBywgDgwyAQnQA/122RogISABesBd2MAgE5AAx8jIyEhzg0rd6pNr6ncga0TW/XpTDcCgEJAAx0hdSLzeQXqk7bHHHmvPAuh/AhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgjwOjo6P7156z9ddWfzcAMGg6e+sCZLOk/g9yJs3ijzrU6u9h11MPtHv0kzmLLvf3mr5TPzM2bRtr96B/LF0w4jOzT5iBBAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEjguLV9+/aybNmydg+AyRKQwHGnG47z588vGzdubI/CAS99Z2d56olNZeyF59sjr/iXrX9fHrh7ffO6Z/fu9ugB9Vj957rnwLCykPhxwELi/ctC4sdWDcdVq1YdFo1+BwezkHgpv/vr15eH/+JPy4+d8xPl1nsfacb12KHW3vnZsuinlzbjGo7rVq8oO3bsaPa7xp/D9FhIvH+YgQSGnhlHpqOGYzceTzv9Tc1r15oV7yv/+cy/l0/f8tvNuMbj3Llzywknntie8co5NS5hmAhIYGhNNhzrjNsgb5s3b27/JMy0ehm6zj7WcKwzkRse/admdvbKlR9pzyhl1VWXlHtu/0QzrrONf/aV/yh/teXb5dd+57bmWHX3p9a1IxgOAhIYOmYcmUk1Hj91/183l7O7rv7lj+2fjayzjnXG8Y+/8ORBl6rfuezn9+/XEK3fq4RhISCBofPwww+XLVu2tHswPZ+8+/Nl5A2ntXsHnHfhO9pRKZ/4k8+XM+e/pd074KJ3HbjLv17qhmEhIIGhs3LlymYWcsOGDc330WA63vimN7ejg73+1JF2tO+cHz2zHU3s5f82A8nwEJDA0Fq+fHkZGxtrQnLevHnt0cPVuzoHeVuyZEn7J6FX9uz6Xjua2EmvP6UdweATkMDQqyFZZyTXr19/1JCE2WQGkmEiIIHjRvfStpCkF8xAMkwEJHDcEZLMtBPmvLYdTexoM5DP/dc3mkWy6+ZubQaBgASOW92QhOl6aRKXpyeagazrTF75jre1ezAYBCQATNPJk7g8faQZyD/4+Eeap9zUhcnrmpHjn2AD/UxAAsA0TXUG8snHv9g8saYuTH7CCXPKnt2723egvwlIAJimqc5A1kcj1ifWVHv27DIDycAQkABwiHMWnV8WLlxYzln8U+2Rw5379gub9+sjDicKvwXnLGr+PfWcH5nEYuNmIBkUnb11FdpZUh/yP5Nm8UcdavX3sOupB9o9+smcRZf7e03fqZ8Zm7aNtXscK2tWvK9s/eqXy2ef+Ndy8uss+XMk9S51n5n9wQwkAPSB7ncgzUIyCAQkAPSBuv5jvRRu9pFBICABoA/UcGxmIPfsMgtJ3xOQANAHujOQlbux6XcCEgD6QHcGEgaBgASAHqix+HPnn7X/Gdh/s+kLzfH3Lh5t9lf94qXNPvQjy/gcByzj078s40M/sowP/coyPv3DDCQAABEBCQBAREACABARkAAARAQkAAARAQkAQERAAgAQEZAAAEQEJD3xlS3bygVXf7Rc+uGb2iOl3HTnfeW8K3+lWVy7bpevurk8+63n23dfceuGB8vpF3+wef8t77m2vP9X1x12DgAwuzyJ5jjQj0+iueuBh8uH1t7ZjF/6u/vLT35gddn69e3N/qGevOf3y9lnnXnUc7706ZvL4h9/a7s3ODyJhn7kSTT0K0+i6R9mIOmJOSee0I5KOeNd1zZheMG5Z5e7fvP68sjtv1Uufvvb2ndL+Y3b7ilnL7u+Oeect46WW9esKI/edVP5hXdf1J5R9scoADD7BCQ9t2PHjiYGazjW1xqSn/vDG5tYrB7526fLN779fBOVdTbymsvfWc5fuKCJzUuXLG7OqXHpUjYAHBsCkp7YtXtPOypNNNYYPNRV717SjkoTjzUqD3XVzxyYhXziH7/WjgCA2SQg6YlTXndSOyrll967tB0d7NwFZ7WjUt5z4aJ2dLDzxn3v8bkXXmxHAMBsEpD0xM7vvNyOJmf8dybH+964mczdew6MAYDZIyDpifFB+L/f/792NLHxl7zHe+0EYQkAzB4BSU+MD8IffM2R/xqOD8vJzEACAMeGgKQnJjMDOT4sJ5qBfDV1vcnuwuTd7f5Hvty+CwBMhYCk56YzA3k0NR7/6M+/2Cyi3t3qHd8f+Ngnm6feAABTIyDpifEzitOZgTzadyDrepF13cjx6nJBZ7zxDeUzD27e99/9fnsUAEgISHpi/Izisf4O5ILRM8rOl14uL313V3sEAEgISHpuNr8DeSTbtn+znHLySeXkH57THgEAEgKSnpipu7DTZXy+9A9fK9987oXywZ+9eN9/9zXtUQAg0dm7TzuecZ1Opx3NjFn8UYda/T3UG0j6zVf/+evlxBN/aP8zr4+kPuN69+7/KYvHPXHmUPWcl7+7q3k+9qu59MM3Nc/Wfu7Ru8up456G0yv1rnB/r+k39TNj07axdg/6x9IFIz4z+4QZSHqmRuHR4rGq7x8tHqt6zmTi8ZqP39bE4/2/t7ov4hEABpWA5LjwmQcfa7Ybr3l/uXTJ4vYoADAVApKhV9eDrLOPNRxvXHFFexQAmCoByVCr37P80No7y5tPP625dA0ATJ+AZGg9+63nywVXf7T5juS/fW59exQAmC4BydBaf/9fNq/1Lu1Dn4ddN48zBICpsYzPcaBfl/HBMj70J8v40K8s49M/zEACABARkAAARAQkAAARAQkAQERAAgAQEZAAAEQEJAAAEQEJAEBEQAIAEBGQAABEBCQAABEBCQBAREACABARkAAARAQkAAARAQkAQERAAgAQEZAAAEQEJAAAEQEJAEBEQAIAEBGQAABEBCQAABEBCQBAREACABARkAAARAQkAACRzt592vGM63Q67QgAgGNlFvOuYQYSAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiHT27tOOAQDgVZmBBAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAACICEgCAiIAEACAiIAEAiAhIAAAiAhIAgIiABAAgIiABAIgISAAAIgISAICIgAQAICIgAQCICEgAAAKl/D8Rs3D2kn1nXQAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\" width=\"328\" height=\"198\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = countCollisions(m1,m2,v1)\r\n  y = length(ode45('NewtonII',tspan,y0));\r\n  ","test_suite":"%%\r\nm1 = 1;\r\nm2 = 1;\r\nv1 = 1;\r\ny_correct = 3;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 2;\r\nm2 = 1;\r\nv1 = 1;\r\ny_correct = 5;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 17;\r\nm2 = 4;\r\nv1 = 8;\r\ny_correct = 6;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 15;\r\nm2 = 1.5;\r\nv1 = 0.3;\r\ny_correct = 10;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 3;\r\nm2 = 0.03;\r\nv1 = 0.5;\r\ny_correct = 31;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 4500000;\r\nm2 = 4.5;\r\nv1 = 0.55;\r\ny_correct = 3141;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm1 = 1.8e11;\r\nm2 = 18;\r\nv1 = 5.2;\r\ny_correct = 314159;\r\ny = countCollisions(m1,m2,v1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np2 = regexprep('11.0010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000','\\.','');\r\nfor k = 2:10\r\n    m2 = rand;\r\n    m1 = 4^k*m2;\r\n    v1 = rand;\r\n    y = countCollisions(m1,m2,v1);\r\n    assert(isequal(dec2bin(y),p2(1:k+2)))\r\nend\r\n\r\n%%\r\np7 = regexprep('3.0663651432036134110263402244652226643520650240155443215426431025161154565220002622436103301443233631','\\.','');\r\nfor k = 2:8\r\n    m2 = rand;\r\n    m1 = 49^k*m2;\r\n    v1 = rand;\r\n    y = countCollisions(m1,m2,v1);\r\n    assert(isequal(dec2base(y,7),p7(1:k+1)))\r\nend\r\n\r\n%%\r\nfiletext = fileread('countCollisions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'classdef'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":46909,"edited_by":46909,"edited_at":"2023-07-22T01:52:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-22T01:47:49.000Z","updated_at":"2023-07-22T01:52:49.000Z","published_at":"2023-07-22T01:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo blocks, which have masses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, slide along a frictionless, semi-infinite track bounded by a stationary wall. Initially block 2 is not moving, and block 1 moves to the left with speed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. All of the collisions are elastic. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to count the collisions between the two blocks and block 2 and the wall. For example, if the blocks each have mass of 1 kg and block 1 initially moves to the left at 0.5 m/s, there will be three collisions: the initial collision, a collision between block 2 and the wall, and a final collision between the blocks. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"198\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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