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:
[tex]C=2\pi r[/tex] [set r = 1.5 m]
⇒ [tex]C=2\pi (1.5)[/tex]
⇒ [tex]C=3\pi[/tex] m
One revolution of the water wheel corresponds to [tex]3\pi[/tex] meters so the angular velocity 15 rmp (revolutions per minute) corresponds to:
[tex]15(3\pi )[/tex] = [tex]45\pi[/tex] [tex]m[/tex]/min
Using this result, the speed of the river in kilometers per hour will be:
[tex]v=\frac{45\pi m }{1 min}[/tex] × [tex]\frac{1 km}{1000 m}[/tex] × [tex]\frac{60 min}{1 h}[/tex]
⇒ [tex]v=8.48230016469[/tex] [tex]km/h[/tex]
⇒ [tex]v[/tex] ≈ [tex]8.5[/tex] km/h
