From a boat approaching Nantucket island, a sailor can see the Brant point light
ID: 2015788 • Letter: F
Question
From a boat approaching Nantucket island, a sailor can see the Brant point light house which sits on the edge of the shore. The sailor knows that the light house is 8.0m tail. Using a compass, he notes that the light house subtends an angle equal to 0.5 degrees.A) How far away is the shore?
B) What angle will be subtended when the sailor is 500m from the shore?
A windmill is turning at 80 rpm.
A) What is the angular speed in radians/sec?
B) How long does it take for the windmill to make 1 revolution?
Explanation / Answer
Question:A windmill is turning at 80 rpm.
A) What is the angular speed in radians/sec?
B) How long does it take for the windmill to make 1 revolution? Solution: (a) Angular speed () of the windmill = 80 rpm = 80 rev/min As we know the conversion 1 rev = 2 rad 1 min = 60 s Then angular speed () of the wind mill = 80 rev/min = (80)(2 rad) / (60 s) = 8.4 rad/s (b) Angular displacement () of wind mill = 1 rev Then time (t) taken to complete one rev is = / t t = / = (1 rev) / (80 rev / min) = 0.0125 min = (0.0125)(60 s) = 0.75 s (a) Angular speed () of the windmill = 80 rpm = 80 rev/min As we know the conversion 1 rev = 2 rad 1 min = 60 s Then angular speed () of the wind mill = 80 rev/min = (80)(2 rad) / (60 s) = 8.4 rad/s (b) Angular displacement () of wind mill = 1 rev Then time (t) taken to complete one rev is = / t t = / = (1 rev) / (80 rev / min) = 0.0125 min = (0.0125)(60 s) = 0.75 s
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