2b:null 2c:["$","title",null,{"children":"Interception calculation | Amit Patel | Observable"}] 31:[] 2f:{"id":"99c94a7673ecf661","slug":"interception-calculation","title":"Interception calculation","thumbnail":"fd3191784b18ec743b4cd9e95dfd00b650250f132914b404e6d868d8ee2fd8e2","access_level":"public","create_time":"$D2019-11-20T22:44:27.035Z","update_time":"$D2019-11-21T02:19:18.146Z","view_time":null,"first_public_time":"$D2019-11-20T23:59:28.157Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"468ec444dc0eb0ae","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":"starter_2024"},"version":123,"publish_version":123,"role":null,"authored":false,"authors":[{"type":"individual","id":"c7764e85dbcadc6d","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":null}],"members":[{"type":"individual","id":"c7764e85dbcadc6d","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"title":"Interception calculation","cells":[{"id":0,"value":"md`# Interception calculation\n\nTarget A at the origin is moving with velocity v1 on course theta; gun at B shoots bullet with velocity v2. At what point C can they collide? To simplify the problem let's assume that A is moving horizontally.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":86,"value":"viewof target_position = slider({\n min: -200, \n max: 600,\n value: -100,\n step: 0.1, \n description: \"Position of target\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":96,"value":"viewof distance = slider({\n min: 0, \n max: 100, \n value: 50,\n step: 0.1, \n description: \"Distance to target vector\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":7,"value":"svg``\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":106,"value":"md`Calculations:\n\n${tex.block`\nv_1 t \\sin \\theta = C_y \\\\\nv_1 t \\cos \\theta = C_x \\\\\nv_2 t = \\sqrt{(C_x - B_x)^2 + (C_y - B_y)^2} \\\\\n`}\n\nThen we can plug in the value of B:\n${tex.block`\nv_2 t = \\sqrt{(C_x - ${B[0]})^2 + (C_y - ${B[1]})^2}\n`}\nand solve for C? or are we solving for t?\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":58,"value":"A = [target_position, 0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":63,"value":"B = [0, distance]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":64,"value":"C = calculateInterception(A, B)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":74,"value":"md`## Calculation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":45,"value":"function calculateInterception(A, B) {\n // TODO: A, B are [x, y] and this function should return another [x, y]\n return [0, 0];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":72,"value":"md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":115,"value":"md`This started when I watched a GDC talk about projectiles; see [the slides](https://shellsphinx.github.io/images/PredictableProjectiles.pdf).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":21,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":69,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"