{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":49825,"title":"Angular Velocity","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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 21px; text-align: left; transform-origin: 384px 21px; 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 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a value of velocity or a set of velocities (in a vector or matrix form) and the radius, determine the corresponding angular velocity in a circular motion.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function omega = ang_vel(v,r)\r\n  omega = alpha*v + pi*r^2;\r\nend","test_suite":"%%\r\nv=2728;\r\nr=17;\r\nv_cor=160.4706;\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n%%\r\nv=[1 2 4;3 7 8];\r\nr=pi;\r\nv_cor=[0.3183 0.6366 1.2732; 0.9549 2.2282 2.5465];\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n%%\r\nv=primes(19);\r\nr=sqrt(3);\r\nv_cor=[1.1547 1.7321 2.8868 4.0415 6.3509 7.5056 9.8150 10.9697];\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-15T15:29:09.000Z","updated_at":"2026-02-19T14:19:41.000Z","published_at":"2021-01-15T15:29:09.000Z","restored_at":null,"restored_by":null,"spam":false,"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\u003eGiven a value of velocity or a set of velocities (in a vector or matrix form) and the radius, determine the corresponding angular velocity in a circular motion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49077,"title":"Velocity Conversion ","description":"Given a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; 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: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n  y = x*fast;\r\nend","test_suite":"%%\r\nx = 11;\r\ny_correct = 17.7027;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 45;\r\ny_correct = 72.4203;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 80;\r\ny_correct = 128.7472;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":8,"created_by":180632,"edited_by":26769,"edited_at":"2022-04-12T14:19:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1666,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T22:04:31.000Z","updated_at":"2026-04-03T03:28:00.000Z","published_at":"2020-12-22T22:04:31.000Z","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\u003eGiven a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42689,"title":"Distance a ball travels after throwing vertically","description":"Calculate the total distance *'d'* (in meters) a ball would travel after *'s'* seconds and starting velocity of *'v'* (in m/s). \"Please note that its not relative distance but total distance travelled\"\r\n\r\ngravity=10 m/s^2\r\n\r\nExample: initial speed = +20, how long does the ball travel after 2.5 sec\r\nd=21.25","description_html":"\u003cp\u003eCalculate the total distance \u003cb\u003e'd'\u003c/b\u003e (in meters) a ball would travel after \u003cb\u003e's'\u003c/b\u003e seconds and starting velocity of \u003cb\u003e'v'\u003c/b\u003e (in m/s). \"Please note that its not relative distance but total distance travelled\"\u003c/p\u003e\u003cp\u003egravity=10 m/s^2\u003c/p\u003e\u003cp\u003eExample: initial speed = +20, how long does the ball travel after 2.5 sec\r\nd=21.25\u003c/p\u003e","function_template":"function d = distance(s,v)\r\nif v-10*s\u003e0\r\nd=((v-s*10)+v)/2*s\r\nelseif 2*v-10*s\u003c0\r\nd=v*v/10\r\nelse\r\nd=v/10*v/2+(s-v/10)^2*10/2\r\nend\r\nend","test_suite":"%%\r\nv = 20;\r\ns=2;\r\nd = 20;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv = 20;\r\ns=2.5;\r\nd = 21.25;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv = 20;\r\ns=12.5;\r\nd=40;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv=50;\r\ns=10;\r\nd=250;\r\n\r\nv=5;\r\ns=5;\r\nd=2.5;\r\nassert(isequal(distance(s,v),d));","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":9199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2015-11-25T15:32:59.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-25T11:24:15.000Z","updated_at":"2026-02-04T17:51:38.000Z","published_at":"2015-11-25T15:29:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the total distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'd'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in meters) a ball would travel after\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e's'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e seconds and starting velocity of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in m/s). \\\"Please note that its not relative distance but total distance travelled\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egravity=10 m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: initial speed = +20, how long does the ball travel after 2.5 sec d=21.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2441,"title":"Bernoulli's Equation","description":"Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\r\n\r\nAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\r\n","description_html":"\u003cp\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/p\u003e\u003cp\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/p\u003e","function_template":"function out = Bernoulli_eq(in,rho)\r\n out = in;\r\nend","test_suite":"%%\r\nin = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 0 0 0 0];\r\nrho = 1.0;\r\nout = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 9.339 8.218 7.057 6.0760];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 0.6 0.8 1 1; 0 0 1 0 0; 10 12 10 14 8];\r\nrho = 1.5;\r\nout = [1 0.6 0.8 1 1; 0.9817 0.8784 1 0.7098 1.1176; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [0 0 0 1 0; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\nrho = 0.75;\r\nout = [4.1896 3.2027 3.6917 1 3.8779; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 1.6 0.8 1 1 0 0 1 1 1.2; 1 1.6 0 1.3 0 1.9 1.8 1.7 0 1.8; 0 12 5 0 8 7.5 7.7 0 11.1 0];\r\nrho = 0.97;\r\nout = [1 1.6 0.8 1 1 2.4397 2.7390 1 1 1.2; 1 1.6 2.4335 1.3 2.0999 1.9 1.8 1.7 1.7741 1.8; 18.466 12 5 15.6113 8 7.5 7.7 11.805 11.1 10.6401];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-16T17:48:45.000Z","updated_at":"2026-01-31T12:50:33.000Z","published_at":"2014-07-16T17:48:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\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\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":49825,"title":"Angular Velocity","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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 21px; text-align: left; transform-origin: 384px 21px; 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 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a value of velocity or a set of velocities (in a vector or matrix form) and the radius, determine the corresponding angular velocity in a circular motion.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function omega = ang_vel(v,r)\r\n  omega = alpha*v + pi*r^2;\r\nend","test_suite":"%%\r\nv=2728;\r\nr=17;\r\nv_cor=160.4706;\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n%%\r\nv=[1 2 4;3 7 8];\r\nr=pi;\r\nv_cor=[0.3183 0.6366 1.2732; 0.9549 2.2282 2.5465];\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n%%\r\nv=primes(19);\r\nr=sqrt(3);\r\nv_cor=[1.1547 1.7321 2.8868 4.0415 6.3509 7.5056 9.8150 10.9697];\r\nassert(isequal(ang_vel(v,r),v_cor))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-15T15:29:09.000Z","updated_at":"2026-02-19T14:19:41.000Z","published_at":"2021-01-15T15:29:09.000Z","restored_at":null,"restored_by":null,"spam":false,"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\u003eGiven a value of velocity or a set of velocities (in a vector or matrix form) and the radius, determine the corresponding angular velocity in a circular motion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49077,"title":"Velocity Conversion ","description":"Given a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; 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: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n  y = x*fast;\r\nend","test_suite":"%%\r\nx = 11;\r\ny_correct = 17.7027;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 45;\r\ny_correct = 72.4203;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 80;\r\ny_correct = 128.7472;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":8,"created_by":180632,"edited_by":26769,"edited_at":"2022-04-12T14:19:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1666,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T22:04:31.000Z","updated_at":"2026-04-03T03:28:00.000Z","published_at":"2020-12-22T22:04:31.000Z","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\u003eGiven a velocity in mph, convert it to km/h. Round the answer to the fourth decimal place.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42689,"title":"Distance a ball travels after throwing vertically","description":"Calculate the total distance *'d'* (in meters) a ball would travel after *'s'* seconds and starting velocity of *'v'* (in m/s). \"Please note that its not relative distance but total distance travelled\"\r\n\r\ngravity=10 m/s^2\r\n\r\nExample: initial speed = +20, how long does the ball travel after 2.5 sec\r\nd=21.25","description_html":"\u003cp\u003eCalculate the total distance \u003cb\u003e'd'\u003c/b\u003e (in meters) a ball would travel after \u003cb\u003e's'\u003c/b\u003e seconds and starting velocity of \u003cb\u003e'v'\u003c/b\u003e (in m/s). \"Please note that its not relative distance but total distance travelled\"\u003c/p\u003e\u003cp\u003egravity=10 m/s^2\u003c/p\u003e\u003cp\u003eExample: initial speed = +20, how long does the ball travel after 2.5 sec\r\nd=21.25\u003c/p\u003e","function_template":"function d = distance(s,v)\r\nif v-10*s\u003e0\r\nd=((v-s*10)+v)/2*s\r\nelseif 2*v-10*s\u003c0\r\nd=v*v/10\r\nelse\r\nd=v/10*v/2+(s-v/10)^2*10/2\r\nend\r\nend","test_suite":"%%\r\nv = 20;\r\ns=2;\r\nd = 20;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv = 20;\r\ns=2.5;\r\nd = 21.25;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv = 20;\r\ns=12.5;\r\nd=40;\r\nassert(isequal(distance(s,v),d));\r\n%%\r\n\r\nv=50;\r\ns=10;\r\nd=250;\r\n\r\nv=5;\r\ns=5;\r\nd=2.5;\r\nassert(isequal(distance(s,v),d));","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":9199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2015-11-25T15:32:59.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-25T11:24:15.000Z","updated_at":"2026-02-04T17:51:38.000Z","published_at":"2015-11-25T15:29:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the total distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'd'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in meters) a ball would travel after\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e's'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e seconds and starting velocity of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in m/s). \\\"Please note that its not relative distance but total distance travelled\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egravity=10 m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: initial speed = +20, how long does the ball travel after 2.5 sec d=21.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2441,"title":"Bernoulli's Equation","description":"Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\r\n\r\nAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\r\n","description_html":"\u003cp\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/p\u003e\u003cp\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/p\u003e","function_template":"function out = Bernoulli_eq(in,rho)\r\n out = in;\r\nend","test_suite":"%%\r\nin = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 0 0 0 0];\r\nrho = 1.0;\r\nout = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 9.339 8.218 7.057 6.0760];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 0.6 0.8 1 1; 0 0 1 0 0; 10 12 10 14 8];\r\nrho = 1.5;\r\nout = [1 0.6 0.8 1 1; 0.9817 0.8784 1 0.7098 1.1176; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [0 0 0 1 0; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\nrho = 0.75;\r\nout = [4.1896 3.2027 3.6917 1 3.8779; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 1.6 0.8 1 1 0 0 1 1 1.2; 1 1.6 0 1.3 0 1.9 1.8 1.7 0 1.8; 0 12 5 0 8 7.5 7.7 0 11.1 0];\r\nrho = 0.97;\r\nout = [1 1.6 0.8 1 1 2.4397 2.7390 1 1 1.2; 1 1.6 2.4335 1.3 2.0999 1.9 1.8 1.7 1.7741 1.8; 18.466 12 5 15.6113 8 7.5 7.7 11.805 11.1 10.6401];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-16T17:48:45.000Z","updated_at":"2026-01-31T12:50:33.000Z","published_at":"2014-07-16T17:48:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\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\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. 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