Question

A Ferris wheel completes 4 revolutions in 10 minutes. The radius of the Ferris wheel is 40 feet.
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

Answer:

5.0in/sec

Step-by-step explanation:

$Circumference = 2\pi r\\\\2 \pi \times 40 ft = 80\pi ft = 253.3274123 ft\\\\= 253.3274123 ft \times 12 \: \frac{inches }{feet} \\\\ = 3015.928947 in\\\\\\10 min = 10 min \times 60 \: sec / min = 600 sec\\\\4 \: revolutions / 10 min = 4 \times 3015.928947\: in / 600 sec \\\\ = 5.0 in/sec$

Answer 2

The linear velocity of the Ferris wheel is 20.1 inches per secnod.

What is the angular velocity of a rotating body?

Suppose the body revolves θ angle in t time then the angular velocity of the body is

ω= θ/t

What is the linear velocity of a rotating body?

Suppose the rotating body covers 's' distance in 't' which is actually 'rθ' distance in 't' time because, s=rθ.

Then the linear velocity of the rotating body is

v=s/t=r(θ/t)=r ω

i.e. v=r ω.

How to solve the problem?

The speed of the Ferris wheel is given by 4 revs in 10 minutes. That means 4(2π) radians in 10 minutes.

Hence, the angular velocity of the Ferris Wheel is

ω= 8π/(10×60) rad/s= π/(75) rad/s

Hence, the linear velocity of the Ferris Wheel is

v=r ω= 40 Feet ( π/(75) rad/s)

= (12×40π)/(75) inch/s

= 20.1062 inch/s

≈20.1 inch/s (rounded to the nearest tenth)

To learn more about the Angular velocity visit- https://brainly.com/question/13649539?referrer=searchResults

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