From ca7445b7772583c0499a669741df2e14ff565338 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Thu, 13 Jan 2011 07:26:57 -0500 Subject: [PATCH] Add recitation 2 problems for Phys 101. --- .../Serway_and_Jewett_8/problem03.24.tex | 12 +++++++ .../Serway_and_Jewett_8/problem03.28.tex | 11 +++++++ .../Serway_and_Jewett_8/problem03.29.tex | 20 ++++++++++++ .../Serway_and_Jewett_8/problem03.36.tex | 28 ++++++++++++++++ .../Serway_and_Jewett_8/problem03.43.tex | 32 +++++++++++++++++++ .../Serway_and_Jewett_8/problem03.63.tex | 30 +++++++++++++++++ 6 files changed, 133 insertions(+) create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.24.tex create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.28.tex create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.29.tex create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.36.tex create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.43.tex create mode 100644 latex/problems/Serway_and_Jewett_8/problem03.63.tex diff --git a/latex/problems/Serway_and_Jewett_8/problem03.24.tex b/latex/problems/Serway_and_Jewett_8/problem03.24.tex new file mode 100644 index 0000000..8ba7025 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.24.tex @@ -0,0 +1,12 @@ +\begin{problem*}{3.24} +Given the vectors $\vect{A}=2.00\ihat+6.00\jhat$ and +$\vect{B}=3.00\ihat-2.00\jhat$, \Part{a} draw the vector sum +$\vect{C}=\vect{A}+\vect{B}$ and the vector difference +$\vect{D}=\vect{A}-\vect{B}$. \Part{b} Calculate $\vect{C}$ and +$\vect{D}$, in terms of unit vectors. \Part{c} Calculate $\vect{C}$ +and $\vect{D}$ in terms of polar coordinates, with angles measured +with respect to the positive $x$ axis. +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Serway_and_Jewett_8/problem03.28.tex b/latex/problems/Serway_and_Jewett_8/problem03.28.tex new file mode 100644 index 0000000..3fbb423 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.28.tex @@ -0,0 +1,11 @@ +\begin{problem*}{3.28} +In a game of American football, a quarterback takes the ball from the +line of scrimmage, runs backward a distance of $10.0\U{yards}$, and +then runs sideways parallel to the line of scrimmage for +$15.0\U{yards}$. At this point, he throws a forward pass downfield +$50.0\U{yards}$ perpendicular to the line of scrimmage. What is the +magnitude of the football's resultant displacement? +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Serway_and_Jewett_8/problem03.29.tex b/latex/problems/Serway_and_Jewett_8/problem03.29.tex new file mode 100644 index 0000000..59bc6ad --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.29.tex @@ -0,0 +1,20 @@ +\begin{problem*}{3.29} +The helicopter view in Fig.~P3.29 shows two people pulling on a +stubborn mule. The person on the right pulls with a force +$\vect{F}_1$ of magnitude $120\U{N}$ and direction +$\theta_1=60.0\deg$. The person on the left pulls with a force +$\vect{F}_2$ of magnitude $80.0\U{N}$ and direction of +$\theta_2=75.0\deg$. Find \Part{a} the single force that is +equivalent to the two forces shown and \Part{b} the force that a third +person would have to exert on the mule to make the resultant force +equal to zero. The forces are measured in units of newtons +(symbolized $\bareU{N}$). +\begin{center} +\begin{asy} +draw((0,0)--(1,1)); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Serway_and_Jewett_8/problem03.36.tex b/latex/problems/Serway_and_Jewett_8/problem03.36.tex new file mode 100644 index 0000000..658bc93 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.36.tex @@ -0,0 +1,28 @@ +\begin{problem*}{3.36} +Three displacement vectors of a croquet ball are shown in Figure +P3.36, where $|\vect{A}| = 20.0\U{units}$, $|\vect{B}| = +40.0\U{units}$, and $|\vect{C}| = 30.0\U{units}$. Find \Part{a} the +resultant in unit-vector notation and \Part{b} the magnitude and +direction of the resultant displacement. +\begin{center} +\begin{asy} +import graph; +import Mechanics; + +real u = 0.1cm; + +Vector a = Vector((0,0), mag=20u, dir=90, "$\vect{A}$"); +a.draw(); +Vector b = Vector((0,0), mag=40u, dir=45, "$\vect{B}$"); +b.draw(); +Vector c = Vector((0,0), mag=30u, dir=-45, "$\vect{C}$"); +c.draw(); + +xaxis("$x$"); +yaxis("$y$"); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Serway_and_Jewett_8/problem03.43.tex b/latex/problems/Serway_and_Jewett_8/problem03.43.tex new file mode 100644 index 0000000..15efaf1 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.43.tex @@ -0,0 +1,32 @@ +\begin{problem*}{3.43} +You are standing on the ground at the origin of a coordinate system. +An airplane flies over you with constant velocity parallel to the $x$ +axis at a fixed height of $7.60\E{3}\U{m}$. At time $t=0$, the +airplane is directly above you so that the vector leading from you to +it is $\vect{P}_0=7.60\E{3}\jhat\U{m}$. At $t=30.0\U{s}$, the +position vector leading from you to the airplane is +$\vect{P}_{30}=(8.04\E{3}\ihat+7.60\E{3}\jhat)\U{m}$ as suggested in +Figure P3.43. Determine the magnitude and orientation of the +airplane's position vector at $t=45.0\U{s}$. +\begin{center} +\begin{asy} +import Mechanics; + +real u = 1cm; +real h = 1u; +real d = 8.04/7.6*h; +real dx = 0.2u; + +draw((-dx,0)--(d+dx,0)); +draw((-dx,h)--(d+dx,h)); + +Vector A = Vector();draw((0,0)--(0,h)); +A.draw(); +Vector B = Vector();((0,0)--(d,h)); +B.draw(); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Serway_and_Jewett_8/problem03.63.tex b/latex/problems/Serway_and_Jewett_8/problem03.63.tex new file mode 100644 index 0000000..bdf50f0 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem03.63.tex @@ -0,0 +1,30 @@ +\begin{problem*}{3.63} +A rectangular parallelpiped has dimensions $a$, $b$, and $c$ as shown +in Figure 3.63. \Part{a} Obtain a vector expression for the face +diagonal vector $\vect{R}_1$. \Part{b} What is the magnitude of this +vector? \Part{c} Notice that $\vect{R}_1$, $c\khat$, and $\vect{R}_2$ +make a right triangle. Obtain a vector expression for the body +diagonal vector $\vect{R}_2$. +\begin{center} +\begin{asy} +import graph3; +import Mechanics; + +real u = 1cm; + +real a = 1u; +real b = 1u; +real c = 1u; + +xaxis3(Label("$x$"), 0, 1.5a); +yaxis3(Label("$y$"), 0, 1.5b); +zaxis3(Label("$z$"), 0, 1.5c); + +draw(xscale3(a)*yscale3(b)*zscale3(c)*unitcube); +//Vector A = Vector((0,0,0), +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} -- 2.26.2