When brett and will ride the carousel, brett always selects a horse on the outside row, whereas will prefers the row closest to the center. these rows are 19 ft 5 in. and 12 ft 3 in. from the center, respectively. the angular speed of the carousel is 2.2 revolutions per minute. what is the difference, in miles per hour, in the linear speeds of brett and will?

When the motion is traveling on a straight line, we say that it travels at a certain linear speed or velocity. But when it is in circular motion, the distance it travels is angular. So, this time, we say that it travels at a certain angular speed or velocity. The relationship between linear velocity and angular velocity is:

V = rω

where

V is the linear velocity

r is the radius of the circle

ω is the angular velocity

The final answer should be in miles per hour. To be consistent, let's transform all distances to miles and time to hour.

Brett's distance:

19 ft + 12 in = 19 ft + 12 in (1 ft/12 in) = 20 ft

1 foot is equal to 0.000189394 mile

20 ft * 0.000189394 = 0.00378788 miles

Will's distance:

12 ft + 3 in = 12 ft + 3 (1ft/12in) = 12.25 ft

12.25 ft * 0.000189394 = 0.00232 miles

Next, we convert ω from revolution per minute to radians per minute. One revolution is equal to 2π radians, and 60 minutes is equal to 1 hour:

ω = 2.2 rev/min * (2π rad/1 rev) * (60 min/1 hr)

ω = 264π rad/hour

Now, we can determine the linear velocities of Brett and Will:

Brett's linear velocity = (0.00378788 miles) (264π rad/hour)

Brett's linear velocity = 3.142 miles/h

Will's linear velocity = (0.00232 miles) (264π rad/hour)

Will's linear velocity = 1.924 miles/h