Ethan and Rebecca are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circlar platform, twice as far from the center of the circular platform as Rebecca, who rides on an inner horse. When the merry-go-round is rotating at a constant angular speed, describe Ethans tangential speed?

Ethan's tangential speed is twice as Rebecca's.

Explanation:

Let be the distance from the center of the platform to Rebecca's horse, Rebecca's tangential speed, the Ethan's tangential speed and the merry-go-round angular speed. The distance from the center of the platform to Ethan's horse is . The angular speed is related to the tangential speed by the equation:

Since the angular speed is the same for Ethan and Rebecca, we have that:

Now, solving for we get:

It means that Ethan's tangential speed is twice as Rebecca's.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y