A boy wants to jump onto a moving carousel that is spinning at a rate of 5 revolutions per minute. If the carousel is 64 ft in diameter, how fast must the boy run, in feet per second, to match the speed of the carousel and jump in? Round your answer to two decimal places.
C = pi*D = 3.14 * 64 = 201.1 Ft.
V = 5rev/min * 201.1FT/rev * 1min/60s =
16.76 Ft/s.
To determine the speed at which the boy must run to match the speed of the carousel, we can calculate the linear speed of a point on the edge of the carousel.
First, we need to find the circumference of the carousel. The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Given that the diameter is 64 ft, we can calculate the circumference C = π × 64 ft.
Next, we need to convert the rate of the carousel's revolutions from minutes to seconds. There are 60 seconds in one minute, so the carousel completes 5 revolutions in 60 seconds.
To find the angular speed of the carousel, we divide the number of revolutions by the time taken: 5 revolutions / 60 seconds = 1/12 revolutions per second.
The linear speed of a point on the edge of the carousel is the product of the angular speed and the circumference. Therefore, the linear speed is (1/12 revolutions per second) × (π × 64 ft) = 16π/3 ft/s.
To match the speed of the carousel, the boy must run at the same linear speed. Hence, the boy must run at a speed of 16π/3 ft/s to jump onto the moving carousel.