Question

2.Adam and Beth are visiting an amusement park and have decided to ride the carousel. Adam picked a horse on the outside edge and Beth chose a dragon on the inside, closer to the center.

Part 1: Do Adam and Beth travel the same distance during the ride? Choose a distance that each seat (horse and dragon) sits from the center and use the radius to determine how far each would travel during one rotation.

Part 2: Choose an angle of rotation. Using complete sentences, compare the distance Adam and Beth will travel during this angle measurement.

Answer 1

Part 1:
No they do not travel the same distance.

Let the dragon = 5 feet. Let the horse = 10 feet. Since the carousel is in the shape of a circle. Use the equation for the circumference of a circle to solve for one rotation.

Circumference = 2pi(r)

So for the dragon the distance is 2pi(5) or approximately 31feet.

For the horse, the distance is 2pi(10) or approximately 63 feet.

Answer 2

Part 2:

Let the angle of rotation be 45 degrees. A circle is 360 degrees. So use a proportion to solve for the distance.

For the dragon, we have the proportion 45/360 = distance/(10 pi). To solve for the distance we cross multiply 45 times 10pi and divide by 360. So the distance traveled is approximately 4 feet.

For the horse, we have the proportion 45/360 = distance/20pi. Solving for the distance we get approximately 8 feet.