4.4: Selected Answers

Last updated
Save as PDF

Page ID: 45952

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

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