A wind farm generator uses a two-bladed propellermounted on a pylon at a height of 20 m. The length of eachpropeller blade is 12 m. A tip of the propeller breaks offwhen the propeller is vertical. The fragment flies offhorizontally, falls, and strikes the ground at P. Just beforethe fragment broke off, the propeller was turning uniformly, taking1.2 s for each rotation. In the above figure, the distancefrom the base of the pylon to the point where the fragment strikesthe ground is closest to: a) 130 m b) 160 m c) 120 m d) 140 m e) 150 m

A wind farm generator uses a two-bladed propellermounted on a pylon at a height of 20 m. The length of eachpropeller blade is 12 m. A tip of the propeller breaks offwhen the propeller is vertical. The fragment flies offhorizontally, falls, and strikes the ground at P. Just beforethe fragment broke off, the propeller was turning uniformly, taking1.2 s for each rotation. In the above figure, the distancefrom the base of the pylon to the point where the fragment strikesthe ground is closest to: a) 130 m b) 160 m c) 120 m d) 140 m e) 150 m

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asked 2021-04-24
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A wind farm generator uses a two-bladed propellermounted on a pylon at a height of 20 m. The length of eachpropeller blade is 12 m. A tip of the propeller breaks offwhen the propeller is vertical. The fragment flies offhorizontally, falls, and strikes the ground at P. Just beforethe fragment broke off, the propeller was turning uniformly, taking1.2 s for each rotation. In the above figure, the distancefrom the base of the pylon to the point where the fragment strikesthe ground is closest to:
a) 130 m
b) 160 m
c) 120 m
d) 140 m
e) 150 m

Answers (1)

2021-04-26
To find the velocity of the propeller:
find the cricumference of the propeller blade:
\(\displaystyle\pi{r}^{{{2}}}=\pi{\left({12}^{{{2}}}\right)}={144}\pi\)
if it travels this distance in 1.2 seconds:
\(\displaystyle{v}={144}\frac{\pi}{{1.2}}={120}\pi\frac{{m}}{{s}}\)
The total height is 32 m, so use equation of motion todetermine the time of flight:
d = 32 m
\(\displaystyle{a}\frac{=}{{9.8}}\frac{{m}}{{s}^{{{2}}}}\)
t = ?
\(\displaystyle{V}_{{{i}}}={0}\)
\(\displaystyle{d}={V}{t}+\frac{{1}}{{2}}{a}{t}^{{{2}}}={2.55}\) seconds
now put this into \(\displaystyle{V}_{{{o}}}=\frac{{x}}{{t}}\) and solve for x:
\(\displaystyle\frac{{V}_{{{o}}}}{{t}}={x}={120}\frac{\pi}{{2.55}}={147.8}{m}\)
so this would correspond to e).
0

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