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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Katie McDaniel and Calman \+
Lankton" }}{PARA 0 "" 0 "" {TEXT -1 7 "p.96 #5" }}{PARA 0 "" 0 "" 
{TEXT -1 337 "An object of mass 5kg is given an initial downward veloc
ity of 50 m/sec and then allowed to fall under the influence of gravit
y.  Assume that the force in newtons (N) due to air resistance is -10v
 where v is the velocity of the object.  If the object is initially 50
0 m above the ground, determine when the object will strike the ground
?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 28 "the mass of the ball is 5 kg" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "m:=5;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"mG\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "the force du
e to gravity is 9.81 m/sec2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "g:=9.81;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG$\"$\")*!\"#" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "this is the solution to the diffe
rential equation: m(dv/dt)=mg-10v, which gives the equation of the vel
ocity" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dsolve(\{diff(v(t)
,t)=((m*g-10*v(t))/m),v(0)=50\},v(t));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%\"vG6#%\"tG,&$\"++++0\\!\"*\"\"\"-%$expG6#,$F'!\"#$\"+++]4X!
\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "we differentiated the velo
city to find the position." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
69 "dsolve(\{diff(x(t),t)=4.905000000+45.09500000*exp(-2*t),x(0)=0\},x
(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"xG6#%\"tG,(-%$expG6#,$F'
$!\"#\"\"!$!+++vaA!\")F'$\"+-++0\\!\"*$\"+++vaAF2\"\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 94 "we set the position equal to 500, which i
s the distance to the ground, and solved for time, t." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "solve(-22.54750000*exp(-2.*t)+4.905
000002*t+22.54750000=500);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+>f*R
t*!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "it took 97.3 seconds fo
r the ball to hit the ground." }}}}{MARK "0 2 0" 337 }{VIEWOPTS 1 1 0 
3 2 1804 }