Question

How do I complete this question on arc length?

Answer 1

Answer:

v ≈ 8.5 km/h

Step-by-step 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:

$v=\frac{45\pi m }{1 min}$ ×  $\frac{1 km}{1000 m}$ × $\frac{60 min}{1 h}$

⇒ $v=8.48230016469$  $km/h$

⇒ $v$ ≈ $8.5$ km/h

Answer 2

Answer:

≈ 8 km per hour

Step-by-step explanation:

C = $\pi$ d

C = $\frac{66}{7}$

Velocity = $\frac{66}{7}$ × 15 = $\frac{990}{7}$ ( meters per minute ) = $\frac{0.99}{7}$ × 60 ≈ 8.5 km/h