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 1 in. 19 ft 1 in. and 11 ft 11 in. 11 ft 11 in. from the center, respectively. The angular speed of the carousel is 2.72.7 revolutions per minute. What is the difference, in miles per hour, in the linear speeds of Brett and Will?

the difference, in miles per hour, in the linear speeds of Brett and Will;

∆v = 1.38 mph

Explanation:

Given;

Angular speed w = 2.7 revolutions per minute

Converting to revolutions per hour

w = 2.7 * 60 revolutions per hour

w = 162 rev/hour

Linear speed v = angular speed * 2πr

the difference, in miles per hour, in the linear speeds of Brett and Will;

∆v = w * 2π (r1 - r2)

r1 = Brett radius in miles

r2 = Will radius in miles

r1 = 19ft 1in = (19*12 + 1) = 229 in

r1 = 229 * 1.57828283 * 10^-5 miles

r2 = 11 ft 11 in = (11*12 + 11) = 143 in

r2 = 143 * 1.57828283 * 10^-5 miles

Substituting the values;

∆v = 162 * 2π * (229-143) * 1.57828283 * 10^-5 mph

∆v = 1.38 mph