Question

Use this scenario: 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 counter clockwise.What is the coordinates of the child after 125 seconds?

Answer 1

The coordinates of the child after 125 seconds are approximately (0.866, 0.500).

Step-by-step explanation:

To find the coordinates of the child after 125 seconds, we need to determine the angle of rotation and the distance from the center of the carousel. Since the carousel takes 1 minute to revolve once around, it completes 2π radians of rotation in 60 seconds. Therefore, in 125 seconds, it will rotate by an angle of (125/60) * 2π = (25/12)π radians.

The child enters at the due north position, which corresponds to an angle of π/2 radians. Adding the angle of rotation, the new angle is (25/12)π + π/2 = (49/12)π radians. The distance from the center of the carousel remains the same.

Using the angle and distance, we can find the new coordinates using trigonometric functions. The x-coordinate is given by x = radius * cos(angle) and the y-coordinate is given by y = radius * sin(angle). Plugging in the values, we get:

x = 1 * cos((49/12)π) = 0.866

y = 1 * sin((49/12)π) = 0.500

Therefore, the coordinates of the child after 125 seconds are approximately (0.866, 0.500).