A water wheel has a 10ft radius. To get a good approximation to the speed of a river, you count the revolutions of the wheel and find that it makes 14 revolutions per min. What is the speed of the river?
Answer: 10 mph
how to figure this problem out?
2007-01-19 05:15:43 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The circumference is 2Pi*R = 2*3.14*10 = 62.8 ft. The river flows at 14 time that distance per minute = 879 ft/min = 52752 ft/hr = 9.99 mph = 10.0 mph
2007-01-19 05:21:11 · answer #1 · answered by catarthur 6 · 2⤊ 0⤋
Circumference of waterwheel = 2 pi r = 20 pi feet
So in 14 revolutions, it the river travels under it a distance of
20 pi *14 = 280pi feet
So speed of river is 280 pi feet per minute.
= 280pi *60 feet per hour
= (280* pi*60)5280 miles per hour
= 9.9996 mph approximately = 10 mph
2007-01-19 05:35:50 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
.
This can be solved using some formulae from physics:
Linear Velocity = Radius x Angular Velocity => v = r.ω
Angular Velocity = 2 x pi x Frequency => ω = 2π.ν
ω = 2π.ν
ω = 2 x (22/7) x (14 x 60)
[As speed is required in terms of hours but frequency is in terms of minutes. There are 60 minutes in 1 hour.]
ω = 5280 radians per hour
v = r.ω
v = [ 10 x (1/5280) ] x 5280 [ As speed is required in terms of miles but the radius is in terms of feet. There are 5280 feet in 1 mile.]
v = 10 miles per hour
.
2007-01-19 05:41:56 · answer #3 · answered by Preety 2 · 0⤊ 0⤋
determine circumference of the water wheel.
C = 2πr
C = 2 (3.14) 10'
C = 62.8'
This turns 14 times per minute, so the river is flowing
14 * 62.8 ft/minute
879.2 ft/minute
879.2 ft/minute*60min/hr * 1mile/5280 ft = 9.99 mile/hour
2007-01-19 05:22:02 · answer #4 · answered by bequalming 5 · 0⤊ 0⤋