A wind farm generator uses a two-bladed on a pylon at a height of 20 m as shown

Question

A wind farm generator uses a two-bladed on a pylon at a height of 20 m as shown in the figure. The width of the pylon is very narrow and the length of each propeller blade is 12m. A tip of the propeller breaks off just when the propeller is vertical. The fragment flies off horizontally falls and strikes the ground at point P with negligible air resistance. Just before the fragment broke off the propeller was turning uniformly taking 1.2 s for each rotation. How far is point P from the base of the pylon?

Explanation / Answer

Let

u be the horizontal velocity of the fragment,

P be the period of the propeller's motion,

s be the horizontal distance it travels,

h = gt^2 / 2
t = sqrt(2h / g)
s = u*t = u *sqrt(2h / g)
u = 2pi *r / P
s = (2pi* r / P) sqrt(2*h / g)
s = (2pi r / P) sqrt(2[ h0 +/- r ] / g)
depending whether the propeller tip is vertically above or below the pivot.
s = (2pi * 12 / 1.2) sqrt(2[ 20 + 12 ] / 9.81)
= 160m to 3 sig. fig.

Hence the correct Answer is 160m

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