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

The wheel will travel 900 yards.

Step-by-step explanation:

To find the distance the wheel will travel, we need to multiply the number of rotations by the circumference of the wheel. In this case, the wheel completes 1,000 rotations and has a circumference of 0.9 yards. So, the distance traveled will be:

Distance = Number of Rotations * Circumference

Distance = 1,000 * 0.9

Distance = 900 yards

Therefore, the wheel will travel 900 yards.

Answer 2

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(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=(d)/(2)=(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.