Question

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at P. Just before the fragment broke off, the propellor was turning uniformly, taking 1.2 s for each rotation.

In the figure, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to:

Answer 1

The distance from the base of the pylon to the point where the fragment strikes the ground is approximately 24π m, which is approximately equal to 75.4 m.

Step-by-step explanation:

To find the distance from the base of the pylon to the point where the fragment strikes the ground, we need to determine the horizontal distance traveled by the fragment. Since the propeller takes 1.2s for each rotation, it completes 1/1.2 = 5/6 rotations in 1 second. Therefore, the angular velocity of the propeller is (5/6) * 2π rad/s.

The linear speed of the fragment can be found using the formula:

v = rω

where v is the linear speed, r is the length of each propeller blade, and ω is the angular velocity. Plugging in the values, we get:

v = (12 m) * [(5/6) * 2π rad/s] = 20π m/s.

Since the fragment flies off horizontally, the horizontal distance traveled by the fragment is equal to the horizontal component of its velocity multiplied by the time:

d = (20π m/s) * (1.2 s) = 24π m/s.

Therefore, the distance from the base of the pylon to the point where the fragment strikes the ground is approximately 24π m, which is approximately equal to 75.4 m.