{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 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0
256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1
-1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 19 "Relative motion -- " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "Two objec
ts are projected upward. One at time t=0 with initial velocity" }}
{PARA 0 "" 0 "" {TEXT -1 86 "400 ft/s, second at time t=5 with initial
velocity 320 ft/s. The Heaviside(t-5) second" }}{PARA 0 "" 0 ""
{TEXT -1 56 "object's height function provides the five second delay.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "y:=t->400*t-16*t^2; z:=t->Heavi
side(t-5)*(320*(t-5)-16*(t-5)^2);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 26 "plot(\{y(t),z(t)\},t=0..25);" }}}{EXCHG {PARA 0 "" 0
"" {TEXT -1 116 "We can animate this -- we draw circles of radius 25 a
round each projectile -- and let them rise and fall vertically:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cir
c:=y->[1000+25*cos(s),y+25*sin(s),s=0..2*Pi];" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 95 "with(plots,animate); animate(\{circ(y(t)),circ(z
(t))\},t=0..25,view=[0..2000,0..2500],frames=50);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 278 "What does this look like from the point of view o
f the first object? To find out, we subtract the coordinates of the fi
rst object from each of the objects -- of course, we expect the first \+
object then to seem stationary at the origin -- but how will the secon
d one seem to move?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 111 "Note that because the second object is always below th
e first one, we need to view in the negative y direction!" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "yy:=t->y(t)-
y(t); zz:=t->z(t)-y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "
animate(\{circ(yy(t)), circ(zz(t))\},t=0..25,view=[0..2000,-2500..0],f
rames=50);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 72 "Problem: Why does the second object start
quickly but seem to slow down?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 5 0" 64 }{VIEWOPTS 1 1 0 1
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }