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14 April, 20:07

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?

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  1. 14 April, 20:10
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    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
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