Question

Angela is riding a scooter around her neighborhood. The front wheel has a diameter of 10 inches and the back wheel has a diameter of 5 inches. The scooter is moving at a speed of 10 inches per second.

As she is riding her scooter, a spider hops onto the front wheel. Angela looks down and thinks that if the praying mantis has a good grip that he will go all the way around the wheel in just 1 second. Is Angela right or wrong? Why?

If she is wrong find the amount of time it will take to go all the way around

Answer 1

i. Angela is wrong. Because the diameter of the wheel is not the distance covered all the way round.

ii. The time is 3.14 seconds.

Explanation:

The font wheel has a diameter of 10 inches. Thus;

radius =
`(diameter)/(2)`

=
`(10)/(2)`

= 5 inches

Circumference of a circle = 2
`\pi`r

⇒ The circumference of the front wheel = 2
`\pi`r

= 2 x
`(22)/(7)` x 5

= 31.4286

The circumference of the front wheel is 31.43 inches.

The total distance to be covered by the mantis = circumference of the front wheel

= 31.43 inches

But,

speed =
`(distance)/(time)`

The scooter moves with a speed of 10 inches per second, so that;

10 =
`(31.43)/(time)`

⇒ time =
`(31.43)/(10)`

= 3.143 s

The time taken to complete a revolution by the mantis is 3.14 seconds.

Therefore,

i. Angela is wrong. Because the diameter of the wheel is not the distance covered all the way round.

ii. The time is 3.14 seconds.