פתרונות ופורומים ל"אלבום פתרונות"- זריקה משופעת

נבטא את זמן התנועה מתוך התנועה האופקית:

                                                                                                                              «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨»«/mspace»«mspace linebreak=¨newline¨»«/mspace»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mi mathvariant=¨bold¨»X«/mi»«mrow»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/menclose»«/mstyle»«/math»

 נכתוב את פונקציית המקום בתלות בזמן  עבור התנועה האנכית:

                                                                                                            «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mi mathcolor=¨#0000FF¨»y«/mi»«mo mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨»y«/mi»«mn»0«/mn»«/msub»«mo mathcolor=¨#0000FF¨»+«/mo»«msub mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨»v«/mi»«mn»0«/mn»«/msub»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathcolor=¨#0000FF¨»t«/mi»«mo mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathcolor=¨#0000FF¨»a«/mi»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨»t«/mi»«mn»2«/mn»«/msup»«mspace linebreak=¨newline¨»«/mspace»«mi mathcolor=¨#0000FF¨»y«/mi»«mo mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨»v«/mi»«mrow»«mn»0«/mn»«mi»y«/mi»«/mrow»«/msub»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathcolor=¨#0000FF¨»t«/mi»«mo mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathcolor=¨#0000FF¨»g«/mi»«mo mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨»t«/mi»«mn»2«/mn»«/msup»«mspace linebreak=¨newline¨»«/mspace»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mspace linebreak=¨newline¨»«/mspace»«/mstyle»«/math»

נציב את ביטוי זמן התנועה שמצאנו מהתנועה האופקית בפונקציית המקום זמן של התנועה האנכית:

                                                                     «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mspace linebreak=¨newline¨»«/mspace»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»X«/mi»«mrow»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mfrac»«mi mathvariant=¨bold¨»X«/mi»«mrow»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mspace linebreak=¨newline¨»«/mspace»«mspace linebreak=¨newline¨»«/mspace»«mspace linebreak=¨newline¨»«/mspace»«/mstyle»«/math»

ונקבל את משוואת המסלול של גוף הנע בזריקה משופעת:

                                                                           «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨28px¨»«mspace linebreak=¨newline¨»«/mspace»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»tan«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»X«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/menclose»«mspace linebreak=¨newline¨»«/mspace»«/mstyle»«/math»

נציב את נתוני התנועה הבליסטית ונמצא הגובה של הכדור בקו השער x=d:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tan«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tan«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»55«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»11«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨».«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»55«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»15«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»