Angle of Rotation The restaurant at the top of the Space Needle in Seattle, Washington, is circular and has a radius of 47.25 feet. The dining part of the restaurant revolves, making about one complete revolution every 48 minutes. A dinner party, seated at the edge of the revolving restaurant at 6:45 P.M., finishes at 8:57 P.M.
(a) Find the angle through which the dinner party rotated.
(b) Find the distance the party traveled during dinner.
a)
To find:
The angle by which the dinner party is rotated from 6-45 P.M to 8-57 P.M.
Answer to Problem 1PS
Solution:
Explanation of Solution
Given,
The radius of the circular restaurant
Time of one complete revolution of the dining part
Duration of the dinner party is from 6-45 P.M to 8-57 P.M.
The party between 6-45 P.M to 8-57 P.M corresponds to the duration of 2 hours and 12 minutes or 132 minutes.
First let us calculate the angle by which the dinner party is rotated in a minute.
Angle by which the dinner party rotated in
Thus, the angle by which the dinner party rotated in.
Now, the angle by which the dinner party rotated in 132 minutes is,
Therefore, the dinner party was rotated through the angle of
b)
To find:
The distance by which the party travelled during dinner.
Answer to Problem 1PS
Solution:
816.01feet
Explanation of Solution
Given,
The radius of the circular restaurant
Time of one complete revolution of the dining part
Duration of the dinner party from 6-45 P.M to 8-57 P.M.
The dinner party was rotated by the angle of
Thus, the dinner party completes two full rotations
Thus, two full rotation corresponds to twice the circumference of the circular dinner party and a
Thus, total distance is given by,
Therefore, the dinner party was rotated by the distance of 816.01feet.
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Chapter 4 Solutions
Precalculus (MindTap Course List)
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