{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo nt 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 128 0 128 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 128 1 2 1 2 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "osage.mws 9/22/97" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 155 "An osage orange is whipped by the wind into falling 60 ft while traveling 35 f eet across a road and striking the side of a car. (20 m down, 12 m lat erally)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Use turbulent drag Fd = 1/2 density area v^2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "Drag force (x) = 1/2 Cd d ensity area v vx, and ditto for y. " }}{PARA 0 "" 0 "" {TEXT -1 41 "(t ake Cd = 1/2, air density = 1.2 kg/m^3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "v = vwind - vosage" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "MKS units throughout." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "r estart;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Vw:= 20; R:=1/20;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "C:=1/4*Pi*R ^2*12/10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "m:=4/3*Pi*R^3* 1000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "cm:=C/m;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Vx:=Vw-velx(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Vy:=vely(t);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 46 "eqx1:=Diff(velx(t),t) = cm*sqrt(Vx^2+Vy^2)*Vx; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "eqy1:=Diff(vely(t),t) = -98/10-cm*sqrt(Vx^2+Vy^2)*Vy;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "eqx2:=Diff(x(t),t) = velx(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eqy2:=Diff(y(t),t)=vely(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "sol:=dsolve(\{eqx1,eqy1,eqx2,eqy2,velx(0)=0,vel y(0)=0,x(0) = 0,y(0)=20\},\{velx(t),vely(t),x(t),y(t)\},numeric);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "odeplot(sol,[t,x(t)],0..3,nu mpoints=100,title=`x vs t`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "E stimate distance traveled from area under Vx vs t" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "odeplot(sol,[t,y(t)],0..3,numpoints=100,titl e=`y vs t`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "odeplot(sol ,[x(t),y(t)],0..3,numpoints=100,title=`y vs x`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Estim ate y-distance based on area under Vy vs t" }}{PARA 0 "" 0 "" {TEXT -1 69 "Looks like it takes 30 m/s (67 mph) wind to approximately do th e job." }}}}{MARK "1 0 0" 6 }{VIEWOPTS 1 1 0 1 1 1803 }