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$\begin{array}{l}{\text { If a signal can travel in a cable at } 80 \% \text { of the speed of }} \\ {\text { light, what length of cable, in inches, represents } 1 \text { ns? }}\end{array}$

$\text { Speed }=\frac{\text { distance }}{\text { time }}$

$\text { distance }=\text { Speed } * \text { time }$

(1) $\text { speed }=\frac{80}{100}*3*10^8=2.4*10^8 m/s$

(2) $\text { time }=1 n s= 10^{-9} s$

$\text { distance }=2.4 * 10^{8} * 10^{-9}=0.24 m\Rightarrow 1 Inch=2.54 cm$

$\text {distance}\Rightarrow \text {Length of cable}=0.24m*\frac{1 cm}{10^{-2}}=24 cm$

$\text {Length of cable }=24 cm*\frac{1 Inch}{2.54 cm}=\frac{24}{2.54}Inch=9.45 Inch$

$\begin{array}{l}{\text { Some species of bamboo can grow } 250 \mathrm{mm} / \mathrm{day} \text { . }} \\ {\text { Assume individual cells in the plant are } 10 \mu \mathrm{m} \text { long. }}\end{array}$

$\begin{array}{l}{\text { How long, on average, does it take a bamboo }} \\ {\text { stalk to grow 1 cell length? }}\end{array}$

$\text {rate of growth}=\frac{\text{length}}{\text{time}}$

$\text { rate of growth }=\frac{250 mm}{day}=\frac{250*10^{-3}}{24*60*60 s}=2.9*10^{-6} m/s$

$\text { Length }=10 \mu \mathrm{m}=10*10^{-6}=10^{-5} m$

$\text { time (s) }=\frac{\text Length (m)}{\text rate of growth (m/s)}(s)=\frac{10^{-5}}{2.9*10^{-6} m/s}=3.45 Secand$

$=3.45 S$

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