Question

The wheel in G.O unicycle has a circumference of 0.9 yards. How far will he travel if the wheel on his unicycle completes 1,000 rotations

Answer 1

Answer:

He will travel 2,826 yards approximately, after the wheel completes 1,000 rotations.

Step-by-step explanation:

How far it travels refers to the arc length of the circular movement.

The arc length is defined as

$s= \theta r$

Where $\theta$ is the angle of rotation and $r$ is the radius of the circle.

Now, from the problem we know that the wheel completes 1,000 rotations. We also now that 1 rotation is $2 \pi$, this means that 1,000 rotations would be

$1000\frac{2 \pi}{1}=2000 \pi$

On the other hand, we know that the circumference is 0.9 yards, that means the radius is half of it, by definition

$r=\frac{d}{2}=\frac{0.9yd}{2}=0.45yd$

Replacing all values, we have

$s= \theta r=2000 \pi (0.45yd)$

But, $\pi = 3.14$, then

$s= 2000 (3.14) (0.45yd)=2,826 yd$

Therefore, he will travel 2,826 yards approximately, after the wheel completes 1,000 rotations.