Question

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 is the position of the child after 30 seconds?

1) (0, 0.5)
2) (0.5, 0)
3) (0, -0.5)
4) (-0.5, 0)

Answer 1

After 30 seconds, which represents half of a full revolution or a 180-degree rotation, the child's position on a counterclockwise rotating carousel starting at (0,1) would be (0, -0.5). So, the correct answer is option 3.

Step-by-step explanation:

The question concerns the position of a child on a carousel after a certain time has passed. The carousel rotates counterclockwise and takes one minute to make a full revolution. The child begins at the point (0,1), which is on the north side of the carousel.

To find the position after 30 seconds, we need to determine what fraction of a full circle 30 seconds represents. Since the carousel takes 60 seconds to complete a revolution, 30 seconds is half of a full revolution or 180 degrees.

In terms of Cartesian coordinates, a 180-degree rotation from the point (0,1) would move the point to (0,-1). Therefore, the correct answer is (0, -0.5), assuming the carousel has a radius of 1.