Question

A child is sitting at the edge of a merry-go-round that has a 3m radius. If the merry-go-

round rotates through 120 degrees, how far does the child end up from his starting
point. Note that you are trying to find the straight line distance from the starting point to
the ending point, not the distance around the circle that the child traveled.

Answer 1

Answer: To find the distance the child travels, we can use the arc length formula: s = r * θ, where s is the arc length, r is the radius of the circle, and θ is the angle of rotation in radians. Since the merry-go-round has a radius of 3m and rotates through 120 degrees, we can convert the angle to radians by multiplying by pi/180.

120 degrees * pi/180 = 2pi/3 radians

Now we can plug in the values into the arc length formula:

s = r * θ

s = 3 * (2pi/3)

s = 2pi

The distance the child travels is 2pi meters, which is the circumference of the circle.

Explanation: