3.5: Selected Answers
- Page ID
- 45954
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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 t2 = 1.86 s
2 v1 = 11.2 m/s
3 \(\delta\)rx = 8.3 m
4 v1 = 3.28 m/s
5 v1 = 31.4 m/s
6 The ball hits people in the stands behind home plate. (It sails 10.7 m above home plate.)
7 \(\theta\) = 44°
8 \(\theta\) = 20.1°, 68.8°
9 \(\theta\) = 18.6°, 77.2°
10 No.
11 Yes, as long as the cannon is set to 16.4°.
12 t2 = 0.56 s
13 t2 = 3.22 s
14 t2 = 3.22 s
15 335 m from home
16 t2 = 40 s a = 0.15 m/s2
17 52.6 m from ship
18 25.7 m from ship
19 t2 = 33.5 s \(\theta\) = 188° from line initially between ship and man
20 \(\mu\)s ≥ 0.256
21 a = 0 m/s2
22 a = 0.94 m/s2
23 m = 65.2 kg
24 Fsf = 56 N
25 Fsf = 186 N up
26 a = 1.39 m/s2 down
27 a = 0.84 m/s2
28 m = 51.4 kg
29 t2 = 7.4 s
30 r2x = 14 m
31 \(\mu\)k = 0.085
32 F = 270 N
33 F = 55.9 N
34 a = 0.73 m/s2
35 a = 0.66 m/s2
36 a = 0 m/s2
37 Fmax = 980 N
38 Fmax = 359 N
39 Fmax = 947 N
40 Fmin = 210 N
41 a. r2 = 2.23 m b. t2 = 1.49 s
42 a. v2 = 2.52 m/s b. r2 = 3.78 m
43 m = 51.4 kg
44 a. r2 = 14 m b. t2 = 1.75 s
45 v2 = 27 m/s
46 \(\mu\) = 0.14
47 v2 = 14.9 m/s
48 v2 = 8.89 m/s
49 v2 = 14.3 m/s
50 \(\theta\) = 56°
51 v2 = 5.8 m/s
52 v2audi = 12.8 m/s
53 v2audi = 4.86 m/s