4.4: Selected Answers
- Page ID
- 45952
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1 v3 = 8.83 m/s
2 t3 = 55.5 s
3 r2 bmw = 51.7 m
4 t2 bmw = 30 s
5 v2 bmw = 74.1 m/s
6 r2 bmw = 71.5 m
7 t2 bmw = 2.8 s
8 t = 4.9 s
9 t3 = 11.6 s
10 t2 = 9.3 s
11 t3 = 19.3 s
12 r\(\rho\) = 2.97 m
13 t2 = 28.3 s
14 \(\theta\)2 = 2.1 rad
15 t2 = 30.2 s
16 t2 = 4.46 s
17 v2 = 28.5 m/s
18 \(\theta\)3 = 74.7 rad
19 \(\theta\)3 = 68.4 rad
20 t3 = 108 s
21 t4 = 27.8 s
22 t3 = 26.2 s
23 v2B = 278 m/s
24 r2B = 950 m
25 t4 = 8.96 s
26 t3 = 87.1 s
27 a. v = 14.0 m/s b. v = 16.3 m/s
28 a. \(\omega\) = 0.224 rad/s b. F = 636 N
29 a. F = 14.2 N b. F = 15.7 N
30 a. F = 1114 N b. F = 1810 N
31 F top rope = 44 N
32 \(\theta\) = 76.8°
33 vmax = 17.1 m/s
34 \(\theta\) = 5.8°
35 vmax = 30 m/s
36 too fast!
37 \(\omega\)min = 2 rad/s
38 a. v2 = 746 m/s b. t3 = 107.7 s
39 a. v2 = 194 m/s b. t3 = 27.8 s
40 Fmax = 2125 N
41 v = 13.7 m/s
42 t = 11.6 s
43 a. \(\delta\)r = 29.4 m b. v2 = 12 m/s
44 a. k = 22.6 N/m b. v2 = 17.9 m/s
45 a. k = 19 N/m b. v2 = 20.6 m/s
46 a. d = 4.8 m b. v = 19.8 m/s
47 a. v2 = 3.87 m/s b. \(\delta\)r = 3.4 m
48 a. v2 = 3.91 m/s b. s = 2.13 m
49 a. s = 0.19 m b. v2 = 3.27 m/s