{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 61 "Boat on River - getting as far upstream as possible for \+ vb " 0 " " {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "d_across := 3.5: # distance across the river" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 83 "vb := 4: vr := 5: # change these to see di fferent configurations (but keep vb " 0 " " {MPLTEXT 1 0 84 "d_upstream := d_across*( (vb*sin(theta)-vr) / (vb*c os(theta)) ): # distance upstream" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "deriv_d := diff(d_upstream,theta): # take derivative \+ of distance w/re to angle" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "theta_for_maximum_upstream=evalf((180/Pi)*fsolve(deriv_d,theta,th eta=0.001..(Pi/2)));d_min := eval(d_upstream,theta=fsolve(deriv_d,thet a,theta=0.001..(Pi/2))); # find minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "plot([180*theta/Pi,d_upstream,theta=0..Pi/2],view=[0 ..89,-7..0],thickness=3,numpoints=200,color=black,labels=[\"Theta_upri ver (deg)\",\"D_upriver \"]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 4 "Note" }{TEXT -1 1 " " }{TEXT 262 1 ":" }{TEXT -1 283 " If vb " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 60 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }