Propeller Breaks. A wind farm generator uses a two-bladed propeller mounted on a

Question

Propeller Breaks. A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 18 m. the length of each propeller blade is 11 m. a tip of the propeller breaks off when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at point P. just before the fragment broke off, the propeller was turning uniformly, taking 1.10 s for each rotation. What is the angle with respect to the vertical at which the fragment strikes the ground (think of the moment right before impact)?

Explanation / Answer

The vertical velocity depends only on the height.
The time to hit the ground comes from y = 1/2*g*t^2
so t = sqrt(2*y/g) = sqrt(2*29m/9.8) = 2.43 s

Therefore the vertical velocity = g*t = 9.8*2.43 = 23.814 m/s
Now the horizontal velocity comes from the rotational motion.
We have the angular velocity 2pi/t = 2pi/1.1 = 5.712 rad/s

So the linear velocity at the top = r*5.712 = 11*5.712 = 62.83 m/s
So the angle with respect to the vertical = arctan(vx/vy) = arctan(62.83/23.814) = 69.24 degree

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.