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A boy wants to jump onto a carousel that is spinning at a rate of 14 revolutions per minute. if the carousel is 23 feet in diameter, how fast must the boy run to match the speed of the carousel and jump on?

a. 2.68 feet per second
b. 1,011.59 feet per second
c. 33.72 feet per second
d. 16.86 feet per second

Respuesta :

Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, [tex]\omega=14\ rev/min[/tex]

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

[tex]\omega=14\ rev/min=1.46\ rad/s[/tex]

Radius, r = 11.5 feet

Let v is the velocity. So,

[tex]v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s[/tex]

Hernce, the correct option is (d) "16.86 ft/s"

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