Question 1190375: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 45 seconds?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
1 revolution = 1 minute ---> angular speed is 1 rpm
45 seconds = 45/60 = 3/4 of a minute
I recommend drawing out an xy grid.
Place (0,1) on the grid.
I'm assuming the center of rotation is the origin.
If so, then 3/4 of a full turn means we rotate from (0,1) to (-1,0) to (0,-1) then finally to (1,0).
This is if we move counterclockwise.
The angle of rotation is (3/4)*360 = 270 degrees.
That corresponds to the compass positions of North, West, South, and East in that order.
North = (0,1)
West = (-1,0)
South = (0,-1)
East = (1,0)
Answer: (1,0)
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1),
that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 45 seconds?
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Simple logic shows that counterclockwise rotation will lead the carousel from position (0,1) ("North")
to position (1,0) ("East") in 45 seconds.
Do not accept any other answer.
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