Question

The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?

Answer 1

Answer: 16.33 feet/s

Explanation:

1) Data:

a) circular motion
b) revolutions: 12 rpm
c) r = 15 feet
d) v = ?

2) Formulae:

angular velocity: ω = number of rpm × 2π / 60 seconds

linear velocity: v = ω × r

3) Solution:

ω = 12 × 2π / 60 s = 0.4π rad / s

v = 0.4π rad / s × 13 feet = 5,2 π feet / s ≈ 5,2 (3.14159) feet / s = 16.33 feet/s.

That is the answer.

Answer 2

Answer: There is linear velocity of 75 feet per hour of the children.

Step-by-step explanation:

Since we have given that

Time taken by merry - go - around = 12 times per minute

Distance from the center of the wheel when they are in their seats = 15 feet

We need to find the linear velocity of the children in feet per hour.

According to question,

Linear velocity = $\dfrac{Distance}{Time}$

So, it becomes,

Linear velocity is given by

$\dfrac{15}{12}\times 60\\\\=15\times 5\\\\=75\ feet/hr$

Hence, there is linear velocity of 75 feet per hour of the children.