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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Assigned Week 4 Block 11 b
y Dr. Rickert. Due by 5PM Tuesday, October 5. " }{MPLTEXT 1 0 0 "" }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 1" }}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 44 "Find the size and direction of the vector  7" }{TEXT 
256 1 "i" }{TEXT -1 4 " + 5" }{TEXT 257 1 "j" }{TEXT -1 1 "." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 9 "Problem 2" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Find tw
o vectors that are parallel to the vector 10" }{TEXT 258 1 "i" }{TEXT 
-1 5 " + 20" }{TEXT 259 1 "j" }{TEXT -1 58 ". \nBe sure to explain how
 you know that they are parallel." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "
Problem 3" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Find a vector that is
 perpendicular to the vector 5" }{TEXT 260 1 "i" }{TEXT -1 4 " + 8" }
{TEXT 261 1 "j" }{TEXT -1 60 ". \nBe sure to explain how you know that
 it is perpendicular." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 4" }
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Show how to use the dot product t
o determine the angle between the vectors\n" }{TEXT 262 2 "a " }{TEXT 
-1 3 "= 3" }{TEXT 263 1 "i" }{TEXT -1 4 " + 4" }{TEXT 264 1 "j" }
{TEXT -1 5 " and " }{TEXT 265 1 "b" }{TEXT -1 4 " = -" }{TEXT 266 1 "i
" }{TEXT -1 4 " + 5" }{TEXT 267 1 "j" }{TEXT -1 1 "." }{MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 9 "Problem 5" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Th
e position function of a fly is " }{TEXT 282 1 "r" }{TEXT -1 1 "(" }
{TEXT 285 1 "t" }{TEXT -1 2 ")=" }{XPPEDIT 18 0 "cos(3*t);" "6#-%$cosG
6#*&\"\"$\"\"\"%\"tGF(" }{TEXT -1 0 "" }{TEXT 286 1 "i" }{TEXT -1 3 " \+
+ " }{XPPEDIT 18 0 "sin(4*t);" "6#-%$sinG6#*&\"\"%\"\"\"%\"tGF(" }
{TEXT -1 0 "" }{TEXT 287 1 "j" }{TEXT -1 66 ". \nDetermine the velocit
y and acceleration of the fly at the time " }{TEXT 288 1 "t" }{TEXT 
-1 3 " = " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 4 "/12." }{TEXT 
-1 1 " " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 6" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 110 "An object has an initial speed of 100 me
ters per second, moving so that its path has an angle of elevation of \+
" }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 28 ".\nDetermine the \+
vector with " }{TEXT 268 1 "x" }{TEXT -1 24 "-component equal to the \+
" }{TEXT 269 1 "x" }{TEXT -1 45 "-component of the velocity of the obj
ect and " }{TEXT 270 1 "y" }{TEXT -1 25 "-component \nequal to the " }
{TEXT 271 1 "y" }{TEXT -1 42 "-component of the velocity of the object
. " }{MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 7" }}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 156 "An object starts 40 meters directly above the ori
gin with an initial speed of 100 meters per second, moving so that \ni
ts path has an angle of  elevation of " }{XPPEDIT 18 0 "theta;" "6#%&t
hetaG" }{TEXT -1 28 ". Determine the vector with " }{TEXT 272 1 "x" }
{TEXT -1 24 "-component equal to the " }{TEXT 273 1 "x" }{TEXT -1 46 "
-component of the \nposition of the object and " }{TEXT 274 1 "y" }
{TEXT -1 24 "-component equal to the " }{TEXT 275 1 "y" }{TEXT -1 89 "
-component of the position of the object. \nYour work in Problem 6 may
 be helpful to you. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 8" }}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 170 " An projectile starts at the top of a 40 meter high
 vertical cliff with an initial speed of 100 meters per second, \nmovi
ng so that its path has an angle of  elevation of " }{XPPEDIT 18 0 "th
eta;" "6#%&thetaG" }{TEXT -1 133 ". \n(a) Determine the angle of eleva
tion which will maximize the number of meters from the base of the cli
ff that the object lands.   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "(b) The kinetic energy o
f an object is given by " }{XPPEDIT 18 0 "EK = 1*m*v^2/2;" "6#/%#EKG*&
*(\"\"\"\"\"\"%\"mGF()%\"vG\"\"#F(F(\"\"#!\"\"" }{TEXT -1 8 ", where \+
" }{TEXT 276 1 "m" }{TEXT -1 31 " is the mass of the object and " }
{TEXT 277 1 "v" }{TEXT -1 78 " is the velocity of the object. The pote
ntial energy of an object is given by " }{XPPEDIT 18 0 "EP = m*g*h;" "
6#/%#EPG*(%\"mG\"\"\"%\"gGF'%\"hGF'" }{TEXT -1 8 ", where " }{TEXT 
278 1 "h" }{TEXT -1 31 " is the height above zero, and " }{TEXT 279 1 
"g" }{TEXT -1 57 " is the acceleration due to gravity. Determine the r
atio " }{TEXT 280 2 "EK" }{TEXT -1 2 "/(" }{TEXT 281 5 "EK+EP" }{TEXT 
-1 5 ") at " }{TEXT 289 1 "t" }{TEXT -1 21 "=0 for the projectile" }
{TEXT -1 105 ". Show that this ratio is the same as the square of the \+
tangent of the angle that you found in part (a). " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }