An airplane is flying in a straight line with a velocity of 200 mi/h and an acceleration of 3 mi/h². If the propeller has a diameter of 6 ft and is rotating at an angular rate of 120 rad/s , determine the magnitudes of velocity and acceleration of a particle located on the tip of the propeller.

Question

An airplane is flying in a straight line with a velocity of 200 mi/h and an acceleration of 3 mi/h² . If the propeller has a diameter of 6 ft and is rotating at an angular rate of 120 rad/s , determine the magnitudes of velocity and acceleration of a particle located on the tip of the propeller.

Accepted Answer

[latex]\begin{aligned} v_{P l} & =\left(\frac{200 \mathrm{~mi}}{\mathrm{h}} ight)\left(\frac{5280 \mathrm{~ft}}{1 \mathrm{~mi}} ight)\left(\frac{1 \mathrm{~h}}{3600 \mathrm{~s}} ight)=293.3 \mathrm{~ft} / \mathrm{s} \ a_{P l} & =\left(\frac{3 \mathrm{~mi}}{\mathrm{h}^2} ight)\left(\frac{5280 \mathrm{~ft}}{1 \mathrm{~mi}} ight)\left(\frac{1 \mathrm{~h}}{3600 \mathrm{~s}} ight)^2=0.00122 \mathrm{~ft} / \mathrm{s}^2 \ v_{P r} & =120(3)=360 \mathrm{~ft} / \mathrm{s} \ v & =\sqrt{v_{P l}^2+v_{P r}^2}=\sqrt{(293.3)^2+(360)^2}=464 \mathrm{~ft} / \mathrm{s} \ a_{P r} & =\frac{v_{P r}^2}{ ho}=\frac{(360)^2}{3}=43200 \mathrm{~ft} / \mathrm{s}^2 \ a & =\sqrt{a_{P l}^2+a_{P r}^2}=\sqrt{(0.00122)^2+(43200)^2}=43.2\left(10^3 ight) \mathrm{~ft} / \mathrm{s}^2\end{aligned}[/latex]

Question 12.158: An airplane is flying in a straight line with a velocity of ...

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