(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. 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.30159 .33197 L .34127 .31247 L .38095 .29622 L .42063 .28322 L .44048 .27794 L .46032 .27347 L .48016 .26982 L .5 .26697 L .50992 .26586 L .51984 .26494 L .52976 .26423 L .53472 .26395 L .53968 .26372 L .54464 .26355 L .54712 .26348 L .5496 .26342 L .55208 .26338 L .55332 .26336 L .55456 .26334 L .5558 .26333 L .55704 .26332 L .55828 .26332 L .55952 .26332 L .56076 .26332 L .562 .26332 L .56324 .26333 L .56448 .26334 L .56696 .26338 L .56944 .26342 L .57192 .26348 L .5744 .26355 L .57937 .26372 L .58433 .26395 L .58929 .26423 L .59921 .26494 L .60913 .26586 L .61905 .26697 L .63889 .26982 L .65873 .27347 L .69841 .28322 L .7381 .29622 L .77778 .31247 L .81746 .33197 L Mistroke .85714 .35472 L .89683 .38071 L .93651 .40996 L .97619 .44246 L Mfstroke P P p p .004 w .02381 .57407 m .06349 .53183 L .10317 .49283 L .14286 .45708 L .18254 .42458 L .22222 .39534 L .2619 .36934 L .30159 .34659 L .34127 .32709 L .38095 .31084 L .42063 .29785 L .44048 .29257 L .46032 .2881 L .48016 .28444 L .5 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+ x^2, -5 + 9*x + x^2, -5 + 10*x + x^2}}] ;[o] 2 2 2 -5 - 10 x + x -5 - 9 x + x -5 - 8 x + x 2 2 2 -5 - 7 x + x -5 - 6 x + x -5 - 5 x + x 2 2 2 -5 - 4 x + x -5 - 3 x + x -5 - 2 x + x 2 2 2 -5 - x + x -5 + x -5 + x + x 2 2 2 -5 + 2 x + x -5 + 3 x + x -5 + 4 x + x 2 2 2 -5 + 5 x + x -5 + 6 x + x -5 + 7 x + x 2 2 2 -5 + 8 x + x -5 + 9 x + x -5 + 10 x + x :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureTop = 2; pictureWidth = 403; pictureHeight = 249; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.079365 0.227463 0.007092 [ [(-6)] .02381 .22746 0 2 Msboxa [(-4)] .18254 .22746 0 2 Msboxa [(-2)] .34127 .22746 0 2 Msboxa [(2)] .65873 .22746 0 2 Msboxa [(4)] .81746 .22746 0 2 Msboxa [(6)] .97619 .22746 0 2 Msboxa [(-20)] .4875 .08563 1 0 Msboxa [(20)] .4875 .3693 1 0 Msboxa [(40)] .4875 .51113 1 0 Msboxa [ -0.001 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L .53348 .19028 L .53472 .19026 L .53596 .19025 L .5372 .19024 L .53844 .19023 L .53968 .19023 L .54092 .19023 L .54216 .19024 L .5434 .19025 L .54464 .19026 L .54712 .19029 L .5496 .19034 L .55208 .19041 L .55456 .19048 L .55952 .19068 L .56448 .19093 L .56944 .19123 L .57937 .19201 L .58929 .193 L .59921 .19422 L .61905 .19732 L .63889 .20131 L .65873 .20619 L .69841 .2186 L .7381 .23456 L .77778 .25406 L .81746 .2771 L Mistroke .85714 .3037 L .89683 .33384 L .93651 .36752 L .97619 .40475 L Mfstroke P P p p .004 w .02381 .4473 m .06349 .40653 L .10317 .3693 L .14286 .33561 L .18254 .30547 L .22222 .27888 L .2619 .25583 L .30159 .23633 L .34127 .22037 L .38095 .20796 L .40079 .20309 L .42063 .1991 L .44048 .19599 L .4504 .19478 L .46032 .19378 L .47024 .193 L .4752 .1927 L .48016 .19245 L .48512 .19225 L .4876 .19218 L .49008 .19212 L .49256 .19207 L .4938 .19205 L .49504 .19203 L .49628 .19202 L .49752 .19201 L .49876 .19201 L .5 .19201 L .50124 .19201 L .50248 .19201 L .50372 .19202 L .50496 .19203 L .50744 .19207 L .50992 .19212 L .5124 .19218 L .51488 .19225 L .51984 .19245 L .5248 .1927 L .52976 .193 L .53968 .19378 L .5496 .19478 L .55952 .19599 L .57937 .1991 L .59921 .20309 L .61905 .20796 L .65873 .22037 L .69841 .23633 L .7381 .25583 L .77778 .27888 L .81746 .30547 L Mistroke .85714 .33561 L .89683 .3693 L .93651 .40653 L .97619 .4473 L Mfstroke P P p p .004 w .02381 .40475 m .06349 .36752 L .10317 .33384 L .14286 .3037 L .18254 .2771 L .22222 .25406 L .2619 .23456 L .30159 .2186 L .34127 .20619 L .36111 .20131 L .38095 .19732 L .40079 .19422 L .41071 .193 L .42063 .19201 L .43056 .19123 L .43552 .19093 L .44048 .19068 L .44544 .19048 L .44792 .19041 L .4504 .19034 L .45288 .19029 L .45412 .19028 L .45536 .19026 L .4566 .19025 L .45784 .19024 L .45908 .19023 L .46032 .19023 L .46156 .19023 L .4628 .19024 L .46404 .19025 L .46528 .19026 L .46776 .19029 L .47024 .19034 L .47272 .19041 L .4752 .19048 L .48016 .19068 L .48512 .19093 L .49008 .19123 L .5 .19201 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.69841 .27179 L .7381 .29838 L .77778 .32852 L .81746 .3622 L Mistroke .85714 .39944 L .89683 .44021 L .93651 .48453 L .97619 .5324 L Mfstroke P P p p .004 w .02381 .31965 m .06349 .28952 L .10317 .26292 L .14286 .23987 L .18254 .22037 L .22222 .20442 L .2619 .19201 L .28175 .18713 L .30159 .18314 L .32143 .18004 L .33135 .17882 L .34127 .17782 L .35119 .17705 L .35615 .17674 L .36111 .17649 L .36607 .1763 L .36855 .17622 L .37103 .17616 L .37351 .17611 L .37475 .17609 L .37599 .17608 L .37723 .17606 L .37847 .17606 L .37971 .17605 L .38095 .17605 L .38219 .17605 L .38343 .17606 L .38467 .17606 L .38591 .17608 L .38839 .17611 L .39087 .17616 L .39335 .17622 L .39583 .1763 L .40079 .17649 L .40575 .17674 L .41071 .17705 L .42063 .17782 L .43056 .17882 L .44048 .18004 L .46032 .18314 L .48016 .18713 L .5 .19201 L .53968 .20442 L .57937 .22037 L .61905 .23987 L .65873 .26292 L .69841 .28952 L .7381 .31965 L .77778 .35334 L .81746 .39057 L Mistroke .85714 .43135 L .89683 .47567 L .93651 .52354 L .97619 .57495 L Mfstroke P P p p .004 w .02381 .2771 m .06349 .25051 L .10317 .22746 L .14286 .20796 L .18254 .19201 L .22222 .1796 L .24206 .17472 L .2619 .17073 L .28175 .16763 L .29167 .16641 L .30159 .16541 L .31151 .16464 L .31647 .16433 L .32143 .16408 L .32639 .16389 L .32887 .16381 L .33135 .16375 L .33383 .1637 L .33507 .16368 L .33631 .16367 L .33755 .16365 L .33879 .16365 L .34003 .16364 L .34127 .16364 L .34251 .16364 L .34375 .16365 L .34499 .16365 L .34623 .16367 L .34871 .1637 L .35119 .16375 L .35367 .16381 L .35615 .16389 L .36111 .16408 L .36607 .16433 L .37103 .16464 L .38095 .16541 L .39087 .16641 L .40079 .16763 L .42063 .17073 L .44048 .17472 L .46032 .1796 L .5 .19201 L .53968 .20796 L .57937 .22746 L .61905 .25051 L .65873 .2771 L .69841 .30724 L .7381 .34093 L .77778 .37816 L .81746 .41894 L Mistroke .85714 .46326 L .89683 .51113 L .93651 .56254 L .97619 .6175 L Mfstroke P P p p .004 w .02381 .23456 m .06349 .21151 L .10317 .19201 L .14286 .17605 L .18254 .16364 L .20238 .15876 L .22222 .15477 L .24206 .15167 L .25198 .15045 L .2619 .14946 L .27183 .14868 L .27679 .14838 L .28175 .14813 L .28671 .14793 L .28919 .14786 L .29167 .14779 L .29415 .14775 L .29539 .14773 L .29663 .14771 L .29787 .1477 L .29911 .14769 L .30035 .14768 L .30159 .14768 L .30283 .14768 L .30407 .14769 L .30531 .1477 L .30655 .14771 L .30903 .14775 L .31151 .14779 L .31399 .14786 L .31647 .14793 L .32143 .14813 L .32639 .14838 L .33135 .14868 L .34127 .14946 L .35119 .15045 L .36111 .15167 L .38095 .15477 L .40079 .15876 L .42063 .16364 L .46032 .17605 L .5 .19201 L .53968 .21151 L .57937 .23456 L .61905 .26115 L .65873 .29129 L .69841 .32497 L .7381 .3622 L .77778 .40298 L .81746 .4473 L Mistroke .85714 .49517 L .89683 .54659 L .93651 .60155 L Mfstroke .94769 .61803 m .93651 .60155 L s s P P p p .004 w .02381 .19201 m .06349 .1725 L .10317 .15655 L .14286 .14414 L .1627 .13926 L .18254 .13527 L .20238 .13217 L .2123 .13095 L .22222 .12995 L .23214 .12918 L .2371 .12887 L .24206 .12862 L .24702 .12843 L .2495 .12835 L .25198 .12829 L .25446 .12824 L .2557 .12822 L .25694 .12821 L .25818 .1282 L .25942 .12819 L .26066 .12818 L .2619 .12818 L .26314 .12818 L .26438 .12819 L .26563 .1282 L .26687 .12821 L .26935 .12824 L .27183 .12829 L .27431 .12835 L .27679 .12843 L .28175 .12862 L .28671 .12887 L .29167 .12918 L .30159 .12995 L .31151 .13095 L .32143 .13217 L .34127 .13527 L .36111 .13926 L .38095 .14414 L .42063 .15655 L .46032 .1725 L .5 .19201 L .53968 .21505 L .57937 .24165 L .61905 .27179 L .65873 .30547 L .69841 .3427 L .7381 .38348 L .77778 .4278 L .81746 .47567 L Mistroke .85714 .52708 L .89683 .58204 L Mfstroke .92124 .61803 m .89683 .58204 L s s s P P p p .004 w .02381 .14946 m .06349 .1335 L .10317 .12109 L .12302 .11621 L .14286 .11222 L .1627 .10912 L .17262 .1079 L .18254 .10691 L .19246 .10613 L .19742 .10583 L .20238 .10558 L .20734 .10538 L .20982 .10531 L .2123 .10524 L .21478 .1052 L .21602 .10518 L .21726 .10516 L 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.0786 L .19246 .07865 L .19494 .07871 L .19742 .07879 L .20238 .07898 L .20734 .07923 L .2123 .07954 L .22222 .08031 L .23214 .08131 L .24206 .08253 L .2619 .08563 L .28175 .08962 L .30159 .0945 L .34127 .10691 L .38095 .12286 L .42063 .14236 L .46032 .16541 L .5 .19201 L .53968 .22214 L .57937 .25583 L .61905 .29306 L .65873 .33384 L .69841 .37816 L .7381 .42603 L .77778 .47744 L .81746 .5324 L Mistroke .85714 .59091 L Mfstroke .87449 .61803 m .85714 .59091 L s s s s P P p p .004 w .02381 .06436 m .04365 .05948 L .06349 .05549 L .08333 .05239 L .09325 .05117 L .10317 .05017 L .1131 .0494 L .11806 .04909 L .12302 .04884 L .12798 .04865 L .13046 .04857 L .13294 .04851 L .13542 .04846 L .13666 .04844 L .1379 .04843 L .13914 .04842 L .14038 .04841 L .14162 .0484 L .14286 .0484 L .1441 .0484 L .14534 .04841 L .14658 .04842 L .14782 .04843 L .1503 .04846 L .15278 .04851 L .15526 .04857 L .15774 .04865 L .1627 .04884 L .16766 .04909 L .17262 .0494 L .18254 .05017 L .19246 .05117 L .20238 .05239 L .22222 .05549 L .24206 .05948 L .2619 .06436 L .30159 .07677 L .34127 .09272 L .38095 .11222 L .42063 .13527 L .46032 .16187 L .5 .19201 L .53968 .22569 L .57937 .26292 L .61905 .3037 L .65873 .34802 L .69841 .39589 L .7381 .4473 L .77778 .50226 L .81746 .56077 L Mistroke Mfstroke .85408 .61803 m .81746 .56077 L s s s s s P P p p .004 w .02381 .02181 m .04365 .0187 L .05357 .01749 L .06349 .01649 L .07341 .01571 L .07837 .01541 L .08333 .01516 L .08829 .01496 L .09077 .01489 L .09325 .01483 L .09573 .01478 L .09697 .01476 L .09821 .01474 L .09945 .01473 L .10069 .01472 L .10193 .01472 L .10317 .01472 L .10441 .01472 L .10565 .01472 L .10689 .01473 L .10813 .01474 L .11062 .01478 L .1131 .01483 L .11558 .01489 L .11806 .01496 L .12302 .01516 L .12798 .01541 L .13294 .01571 L .14286 .01649 L .15278 .01749 L .1627 .0187 L .18254 .02181 L .20238 .0258 L .22222 .03067 L .2619 .04308 L .30159 .05904 L .34127 .07854 L .38095 .10159 L .42063 .12818 L .46032 .15832 L .5 .19201 L .53968 .22924 L .57937 .27001 L .61905 .31434 L .65873 .3622 L .69841 .41362 L .7381 .46858 L .77778 .52708 L .81746 .58914 L s .83494 .61803 m .81746 .58914 L s s s s s P P P % End of Graphics MathPictureEnd :[font = subsection; inactive; pageBreak; preserveAspect] The path of a projectile depends on the gravity, initial velocity, and angle. :[font = input; preserveAspect; startGroup] Projectile[2, 3, 40]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureTop = 1; pictureWidth = 422; pictureHeight = 118; endGroup] %! %%Creator: Mathematica %%AspectRatio: .2797 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.214905 0.00666 0.214905 [ [(1)] .23871 .00666 0 2 Msboxa [(2)] .45362 .00666 0 2 Msboxa [(3)] .66852 .00666 0 2 Msboxa [(4)] .88343 .00666 0 2 Msboxa [(0.2)] .01131 .04964 1 0 Msboxa [(0.4)] .01131 .09262 1 0 Msboxa [(0.6)] .01131 .1356 1 0 Msboxa [(0.8)] .01131 .17858 1 0 Msboxa [(1)] .01131 .22156 1 0 Msboxa [(1.2)] .01131 .26455 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .2807 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .23871 .00666 m .23871 .01291 L s P [(1)] .23871 .00666 0 2 Mshowa p .002 w .45362 .00666 m .45362 .01291 L s P [(2)] .45362 .00666 0 2 Mshowa p .002 w .66852 .00666 m .66852 .01291 L s P [(3)] .66852 .00666 0 2 Mshowa p .002 w .88343 .00666 m .88343 .01291 L s P [(4)] .88343 .00666 0 2 Mshowa p .001 w .06679 .00666 m .06679 .01041 L s P p .001 w .10977 .00666 m .10977 .01041 L s P p .001 w .15275 .00666 m .15275 .01041 L s P p .001 w .19573 .00666 m .19573 .01041 L s P p .001 w .2817 .00666 m .2817 .01041 L s P p .001 w .32468 .00666 m .32468 .01041 L s P p .001 w .36766 .00666 m .36766 .01041 L s P p .001 w .41064 .00666 m .41064 .01041 L s P p .001 w .4966 .00666 m .4966 .01041 L s P p .001 w .53958 .00666 m .53958 .01041 L s P p .001 w .58256 .00666 m .58256 .01041 L s P p .001 w .62554 .00666 m .62554 .01041 L s P p .001 w .71151 .00666 m .71151 .01041 L s P p .001 w .75449 .00666 m .75449 .01041 L s P p .001 w .79747 .00666 m .79747 .01041 L s P p .001 w .84045 .00666 m .84045 .01041 L s P p .001 w .92641 .00666 m .92641 .01041 L s P p .001 w .96939 .00666 m .96939 .01041 L s P p .002 w 0 .00666 m 1 .00666 L s P p .002 w .02381 .04964 m .03006 .04964 L s P [(0.2)] .01131 .04964 1 0 Mshowa p .002 w .02381 .09262 m .03006 .09262 L s P [(0.4)] .01131 .09262 1 0 Mshowa p .002 w .02381 .1356 m .03006 .1356 L s P [(0.6)] .01131 .1356 1 0 Mshowa p .002 w .02381 .17858 m .03006 .17858 L s P [(0.8)] .01131 .17858 1 0 Mshowa p .002 w .02381 .22156 m .03006 .22156 L s P [(1)] .01131 .22156 1 0 Mshowa p .002 w .02381 .26455 m .03006 .26455 L s P [(1.2)] .01131 .26455 1 0 Mshowa p .001 w .02381 .01526 m .02756 .01526 L s P p .001 w .02381 .02385 m .02756 .02385 L s P p .001 w .02381 .03245 m .02756 .03245 L s P p .001 w .02381 .04104 m .02756 .04104 L s P p .001 w .02381 .05824 m .02756 .05824 L s P p .001 w .02381 .06683 m .02756 .06683 L s P p .001 w .02381 .07543 m .02756 .07543 L s P p .001 w .02381 .08403 m .02756 .08403 L s P p .001 w .02381 .10122 m .02756 .10122 L s P p .001 w .02381 .10981 m .02756 .10981 L s P p .001 w .02381 .11841 m .02756 .11841 L s P p .001 w .02381 .12701 m .02756 .12701 L s P p .001 w .02381 .1442 m .02756 .1442 L s P p .001 w .02381 .15279 m .02756 .15279 L s P p .001 w .02381 .16139 m .02756 .16139 L s P p .001 w .02381 .16999 m .02756 .16999 L s P p .001 w .02381 .18718 m .02756 .18718 L s P p .001 w .02381 .19578 m .02756 .19578 L s P p .001 w .02381 .20437 m .02756 .20437 L s P p .001 w .02381 .21297 m .02756 .21297 L s P p .001 w .02381 .23016 m .02756 .23016 L s P p .001 w .02381 .23876 m .02756 .23876 L s P p .001 w .02381 .24735 m .02756 .24735 L s P p .001 w .02381 .25595 m .02756 .25595 L s P p .001 w .02381 .27314 m .02756 .27314 L s P p .002 w .02381 0 m .02381 .2797 L s P P 0 0 m 1 0 L 1 .2797 L 0 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.11147 L .60107 .09861 L .63145 .08377 L Mistroke .66183 .06696 L .69221 .04817 L .72259 .0274 L .75298 .00465 L Mfstroke P P p p .004 w .02381 .00465 m .05869 .03076 L .09356 .05461 L .12844 .07618 L .16332 .09548 L .1982 .11251 L .23307 .12727 L .26795 .13976 L .30283 .14998 L .3377 .15793 L .35514 .16105 L .37258 .1636 L .39002 .16559 L .39874 .16637 L .40746 .16701 L .41618 .16751 L .42054 .1677 L .4249 .16786 L .42926 .16799 L .43144 .16803 L .43362 .16807 L .4358 .16811 L .43689 .16812 L .43798 .16813 L .43907 .16814 L .44016 .16814 L .44125 .16814 L .44234 .16814 L .44343 .16814 L .44452 .16814 L .44561 .16814 L .4467 .16813 L .44888 .16811 L .45106 .16807 L .45324 .16803 L .45542 .16799 L .45977 .16786 L .46413 .1677 L .46849 .16751 L .47721 .16701 L .48593 .16637 L .49465 .16559 L .51209 .1636 L .52953 .16105 L .54697 .15793 L .58185 .14998 L .61672 .13976 L .6516 .12727 L .68648 .11251 L .72135 .09548 L Mistroke .75623 .07618 L .79111 .05461 L .82599 .03076 L .86086 .00465 L Mfstroke P P p p .004 w .02381 .00465 m .06349 .03436 L .10317 .06149 L .14286 .08603 L .18254 .108 L .22222 .12737 L .2619 .14417 L .30159 .15838 L .34127 .17 L .38095 .17904 L .40079 .1826 L .42063 .1855 L .44048 .18776 L .4504 .18865 L .46032 .18938 L .47024 .18994 L .4752 .19017 L .48016 .19035 L .48512 .19049 L .4876 .19054 L .49008 .19059 L .49256 .19063 L .4938 .19064 L .49504 .19065 L .49628 .19066 L .49752 .19067 L .49876 .19067 L .5 .19067 L .50124 .19067 L .50248 .19067 L .50372 .19066 L .50496 .19065 L .50744 .19063 L .50992 .19059 L .5124 .19054 L .51488 .19049 L .51984 .19035 L .5248 .19017 L .52976 .18994 L .53968 .18938 L .5496 .18865 L .55952 .18776 L .57937 .1855 L .59921 .1826 L .61905 .17904 L .65873 .17 L .69841 .15838 L .7381 .14417 L .77778 .12737 L .81746 .108 L Mistroke .85714 .08603 L .89683 .06149 L .93651 .03436 L .97619 .00465 L Mfstroke P P P % End of Graphics MathPictureEnd :[font = section; inactive; initialization; pageBreak; preserveAspect; startGroup] Implementation :[font = input; initialization; preserveAspect] *) Projectile[g_, v_, a_] := Module[ {t, A}, A = N[a Degree]; ParametricPlot[ { {Cos[A] t, Sin[A] t}, {v t Cos[A], v t Sin[A] - g t^2 / 2} }, {t, 0, 2 v / g Sin[A]}, AspectRatio -> Automatic ] ] (* :[font = input; initialization; preserveAspect] *) Projectiles[g_, v_, a_List] := Module[ {t, A, T}, A = N[a Degree]; T = Map[ ParametricPlot[ {v t Cos[#], v t Sin[#] - g t^2 / 2}, {t, 0, 2 v / g Sin[#]}, DisplayFunction -> Identity ]&, A ]; Show[T, AspectRatio -> Automatic, DisplayFunction -> $DisplayFunction] ] (* :[font = input; initialization; preserveAspect] *) Projectiles[g_, v_List, a_] := Module[ {t, A, T}, A = N[a Degree]; T = Map[ ParametricPlot[ {# t Cos[A], # t Sin[A] - g t^2 / 2}, {t, 0, 2 # / g Sin[A]}, DisplayFunction -> Identity ]&, v ]; Show[T, AspectRatio -> Automatic, DisplayFunction -> $DisplayFunction] ] (* :[font = input; initialization; preserveAspect; endGroup] *) Projectiles[g_List, v_, a_] := Module[ {t, A, T}, A = N[a Degree]; T = Map[ ParametricPlot[ {v t Cos[A], v t Sin[A] - # t^2 / 2}, {t, 0, 2 v / # Sin[A]}, DisplayFunction -> Identity ]&, g ]; Show[T, AspectRatio -> Automatic, DisplayFunction -> $DisplayFunction] ] (* ^*)