Question

A water wheel has a 15-ft radius. To get a good approximation of the speed of the river, you count the revolutions of the

wheel and find that it makes 18 revolutions per minute (rpm). What is the speed of the river, in miles per hour?
The speed of the river, in miles per hour, is
(Do not round until the final answer. Then round to the nearest hundredth as needed.)

Answer 1

The speed of the river in miles per hour is found by calculating the circumference of the wheel, determining the distance traveled in one minute, and then converting that distance into miles per hour, resulting in 5.68 mph.

Step-by-step explanation:

To find the speed of the river in miles per hour, given the water wheel's radius and revolutions per minute (rpm), we first need to calculate the circumference of the wheel.

This is because the distance one revolution covers is equal to the circumference of the wheel.

The formula for circumference is C = 2πr, where r is the radius. With a radius of 15 feet, the circumference C = 2 * π * 15 ft = 30π ft.

Next, we calculate how far the wheel travels in one minute, which is the circumference times the number of revolutions per minute.

The wheel makes 18 revolutions per minute, so the wheel travels a distance of 18 * 30π ft per minute. Now we can convert feet per minute to miles per hour.

Feet per minute to miles per hour conversion:

1 mile = 5280 feet

1 hour = 60 minutes

So, the speed in miles per hour (mph) is (18 * 30π ft/min) * (1 mile/5280 ft) * (60 min/1 hour)

= (18 * 30π / 5280) * 60 mph.

Simplifying this, we get the speed of the river to be approximately:

(18 * 30π / 5280) * 60 mph

= 5.68 mph

After calculating, we round the final answer to the nearest hundredth as required, giving us a speed of 5.68 mph for the river.