Question

A merry-go-round is rotating at the constant angular speed of 3 RPM counterclockwise. The platform of this ride is a circular disc of radius 24 feet. You jump onto the ride at the location

If θ = −2.1 rad, then what are your xy-coordinates after 2 hours and 7 seconds?

Answer 1

To find your xy-coordinates after 2 hours and 7 seconds on the merry-go-round, convert the time to seconds, calculate the angular displacement, and use the polar coordinate system to find the xy-coordinates.

Step-by-step explanation:

To find your xy-coordinates after 2 hours and 7 seconds on the merry-go-round, we need to consider the angular displacement and the radius of the disc. First, convert 2 hours and 7 seconds to seconds. 2 hours is equal to 7200 seconds, so the total time is 7200 + 7 = 7207 seconds. The angular displacement is given by θ = ωt, where θ is the angular displacement in radians, ω is the angular speed in radians per second, and t is the time in seconds. Plug in the values, θ = (-2.1 rad/s)(7207) = -15193.7 rad.

Next, we can find the xy-coordinates using the polar coordinate system. The x-coordinate is given by x = r * cos(θ), and the y-coordinate is given by y = r * sin(θ), where r is the radius of the disc. Plug in the values, x = (24 ft) * cos(-15193.7 rad) and y = (24 ft) * sin(-15193.7 rad).

Finally, calculate the values using a scientific calculator to get the final xy-coordinates.