Question

How do I complete this question on arc length?

Answer 1

≈ 8 km per hour

Explanation:

C =
`\pi` d

C =
`(66)/(7)`

Velocity =
`(66)/(7)` × 15 =
`(990)/(7)` ( meters per minute ) =
`(0.99)/(7)` × 60 ≈ 8.5 km/h

Answer 2

v ≈ 8.5 km/h

Explanation:

Since the diameter of the wheel is 3 m the radius will be r = 1.5 m.

Use the radius of the water wheel to find it's circumference C:

`C=2\pi r` [set r = 1.5 m]

⇒
`C=2\pi (1.5)`

⇒
`C=3\pi` m

One revolution of the water wheel corresponds to
`3\pi` meters so the angular velocity 15 rmp (revolutions per minute) corresponds to:

`15(3\pi )` =
`45\pi`
`m`/min

Using this result, the speed of the river in kilometers per hour will be:

`v=(45\pi m )/(1 min)` ×
`(1 km)/(1000 m)` ×
`(60 min)/(1 h)`

⇒
`v=8.48230016469`
`km/h`

⇒
`v` ≈
`8.5` km/h