The sprocket assembly on a bicycle consists of a chain and two sprockets on the rear wheel. If the sprocket on the pedal is 9 inches in the diameter , the sprocket on the rear wheel is 6 inches in diameter , and the rear wheel is 26 inches in diameter, how fast is the bicycle traveling mph when the cyclist is pedaling at the 1.2 rev per second.?

I don't know what information to use.

1.2rev/s * 9/6 * 26πin/rev = 147in/s

now just convert that to mi/hr

To solve this problem, we need to understand the relationship between the size of the sprockets and the speed of the bicycle. The speed of the bicycle can be calculated using the formula:

Speed = (Pedal Sprocket Diameter / Rear Wheel Sprocket Diameter) * (Rear Wheel Diameter) * (Pedaling Rate)

Let's plug in the given values:

Pedal Sprocket Diameter = 9 inches
Rear Wheel Sprocket Diameter = 6 inches
Rear Wheel Diameter = 26 inches
Pedaling Rate = 1.2 revolutions per second

We can now substitute these values into the formula to find the speed of the bicycle.

Speed = (9 inches / 6 inches) * (26 inches) * (1.2 revolutions per second)

First, let's simplify the pedal sprocket diameter and the rear wheel sprocket diameter:

Speed = (1.5) * (26 inches) * (1.2 revolutions per second)

Next, let's multiply the rear wheel diameter and the pedaling rate:

Speed = 39 inches per second

Finally, let's convert the speed to miles per hour. There are 12 inches in a foot and 5280 feet in a mile, so we can use these conversion factors:

Speed = (39 inches per second) * (1 foot / 12 inches) * (1 mile / 5280 feet) * (3600 seconds / 1 hour)

By simplifying this expression, we find the speed of the bicycle in miles per hour.

Speed = 1.34 mph

Therefore, the bicycle is traveling at a speed of approximately 1.34 mph when the cyclist is pedaling at 1.2 revolutions per second.

To solve this problem, we need to use the concept of gear ratios. The gear ratio is the ratio of the number of teeth on the driving sprocket (the sprocket on the pedal) to the number of teeth on the driven sprocket (the sprocket on the rear wheel).

First, we need to calculate the gear ratio. The number of teeth on the driving sprocket (D1) is related to its diameter (d1) by the formula:

D1 = d1 / π

Given that the diameter of the driving sprocket is 9 inches, we can calculate its number of teeth:

D1 = 9 / π ≈ 2.87

Next, we need to calculate the gear ratio. The number of teeth on the driven sprocket (D2) is related to its diameter (d2) by the same formula:

D2 = d2 / π

Given that the diameter of the driven sprocket is 6 inches, we can calculate its number of teeth:

D2 = 6 / π ≈ 1.91

The gear ratio (G) is then given by the formula:

G = D1 / D2

Substituting the calculated values, we get:

G ≈ 2.87 / 1.91 ≈ 1.50

Now, we can calculate the speed of the bicycle when the cyclist is pedaling at 1.2 revolutions per second. Since the gear ratio represents the number of revolutions of the pedal sprocket for each revolution of the rear wheel sprocket, the speed of the bicycle (v) is given by:

v = G * v1

where v1 is the linear speed of the cyclist's feet. Given that the diameter of the rear wheel is 26 inches, we can calculate its circumference:

C = π * d3

where d3 is the diameter of the rear wheel. Substituting the values, we get:

C = π * 26 ≈ 81.68 inches

The linear speed of the cyclist's feet (v1) is related to the number of revolutions per second (rpm) by the formula:

v1 = C * rpm

Substituting the values, we get:

v1 = 81.68 * 1.2 ≈ 98.02 inches per second

Finally, we can calculate the speed of the bicycle (v) by multiplying v1 by the gear ratio (G) as follows:

v = G * v1

Substituting the calculated values, we get:

v ≈ 1.50 * 98.02 ≈ 147.03 inches per second

To convert this speed to miles per hour (mph), we need to divide by the number of inches in one mile and the number of seconds in one hour:

1 mile = 63360 inches
1 hour = 3600 seconds

Finally, we can convert inches per second to miles per hour:

v ≈ (147.03 / 63360) * 3600 ≈ 8.36 mph

Therefore, the bicycle is traveling at approximately 8.36 mph when the cyclist is pedaling at 1.2 revolutions per second.