Question

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?

Answer 1

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

∆v = 1.38 mph

Step-by-step 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