Question

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of20 m. The length of each propeller blade is 12 m. A small piece from the tip of thepropeller breaks off the top propeller when the propeller is vertical. At that instant,the angular speed of the propeller is 5.2 rad/s.The fragment flies off horizontally, falls with negligible air resistance, and strikes theground at pointP. How far is pointPfrom the base of the pylon

Answer 1

Answer:

159.37 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

r = Radius = 12 m

Time taken to fall

$s=ut+\frac{1}{2}at^2\\\Rightarrow 0.809=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{(20+12)\times 2}{9.81}}\\\Rightarrow t=2.554\ s$

Speed is given by

$v=r\omega\\\Rightarrow v=12\times 5.2\\\Rightarrow v=62.4\ m/s$

Distance is given by

$s=vt\\\Rightarrow s=62.4\times 2.554\\\Rightarrow s=159.37\ m$

The point P is 159.37 m from the base.