A carousel is in a park. The center of the carousel is 60 feet due south...

  

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A carousel is in a park. The center of the carousel is 60 feet due south of the entrance to the park. The carousel has a diameter of 28 feet and takes 14 seconds to complete one counterclockwise revolution. Simon is riding one of the carousel horses, and starts at the point farthest from the park entrance. Let t= 0 denote this starting point. (a) Draw a diagram with the entrance to the park as the origin, and the y-axis stretching through the center of the carousel. (b) Graph Simon's y-coordinate as a function of time for the interval from t = 0 to t = 28 seconds. (e) Find a function of the form f(t) = A sin(B(t – h)) + k that represents the y-coordinate in feet for Simon as a function of time. (d) Write parametric equations (r(t), f(t)) describing Simon's location at time t. (e) What is Simon's location at t = 10 seconds? (f) What distance around the circle does Simon travel in 10 seconds on the ride? A carousel is in a park. The center of the carousel is 60 feet due south of the entrance to the park. The carousel has a diameter of 28 feet and takes 14 seconds to complete one counterclockwise revolution. Simon is riding one of the carousel horses, and starts at the point farthest from the park entrance. Let t= 0 denote this starting point. (a) Draw a diagram with the entrance to the park as the origin, and the y-axis stretching through the center of the carousel. (b) Graph Simon's y-coordinate as a function of time for the interval from t = 0 to t = 28 seconds. (e) Find a function of the form f(t) = A sin(B(t – h)) + k that represents the y-coordinate in feet for Simon as a function of time. (d) Write parametric equations (r(t), f(t)) describing Simon's location at time t. (e) What is Simon's location at t = 10 seconds? (f) What distance around the circle does Simon travel in 10 seconds on the ride?

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a Here is a diagram with the entrance to the park as the origin and the yaxis stretching through the ... View the full answer