A water wheel has a radius of 15 ft. A river passing through the water wheel turns the wheel at 11 revolutions per minute(rpm). What is the speed of the river in miles per hour?
C = pi*2r = 3.14 * 30 = 94.25 Ft. =
Circumference.
V=11rev/min*94.3Ft/rev^1mi/5280Ft*60min/h = 11.8 mi/h
To find the speed of the river in miles per hour, we need to convert the revolutions per minute to a linear speed.
First, let's find the circumference of the water wheel. The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius.
Given that the radius is 15 ft, we can calculate the circumference as follows:
C = 2π * 15 ft
C = 30π ft
Next, we need to convert the revolutions per minute to feet per minute. Since each revolution of the wheel covers the circumference, the linear speed can be found by multiplying the circumference of the wheel by the number of revolutions per minute.
Linear speed = C * rpm
Linear speed = 30π ft * 11 rpm
Linear speed ≈ 330π ft/min
Finally, let's convert the linear speed from feet per minute to miles per hour. There are 5,280 feet in a mile and 60 minutes in an hour, so:
Speed (in miles per hour) = [(Linear speed in feet per minute) * (1 mile/5,280 feet) * (60 minutes/1 hour)]
Substituting the value of the linear speed we calculated:
Speed (in miles per hour) = [330π ft/min * (1 mile/5,280 feet) * (60 minutes/1 hour)]
Simplifying further, we get:
Speed (in miles per hour) = (330π * 60) / 5,280 mph
Using an approximation for π as 3.14, we can calculate:
Speed (in miles per hour) ≈ (330 * 3.14 * 60) / 5,280 mph
Speed (in miles per hour) ≈ 18.85 mph
Therefore, the speed of the river is approximately 18.85 miles per hour.