A bicycle wheel, diameter 56 cm, is making 45 revolutions in every 10 seconds. At what speed, in kilometer per hour. Is the bicycle travelling?
45 rev/10sec * 56π cm/rev * 1km/100000cm * 3600sec/hr = 28.5 km/hr
192
To find the speed at which the bicycle is traveling, we can follow these steps:
Step 1: Calculate the distance traveled in one revolution.
The distance traveled in one revolution is equal to the circumference of the wheel.
Circumference = π * Diameter
C = π * 56 cm
Step 2: Convert the distance to kilometers.
Since the final speed is required in kilometers per hour, we need to convert the distance to kilometers.
1 kilometer = 1000 meters
1 meter = 100 centimeters
Therefore, to convert centimeters to kilometers, we divide by 100,000.
Distance (km) = C (cm) / 100,000
Step 3: Calculate the total distance traveled in 45 revolutions.
Total distance (km) = Distance (km) * Number of revolutions
Step 4: Calculate the time taken in hours.
The given time is in seconds, so we need to convert it to hours.
1 hour = 60 minutes
1 minute = 60 seconds
Therefore, to convert seconds to hours, we divide by 3,600 (60 * 60).
Time (hours) = Time (seconds) / 3,600
Step 5: Calculate the speed.
Speed (km/h) = Total distance (km) / Time (hours)
Let's calculate the speed:
Step 1:
C = π * 56 cm = 176 cm
Step 2:
Distance (km) = 176 cm / 100,000 = 0.00176 km
Step 3:
Total distance (km) = 0.00176 km * 45 = 0.0792 km
Step 4:
Time (hours) = 10 seconds / 3,600 = 0.00278 hours
Step 5:
Speed (km/h) = 0.0792 km / 0.00278 hours ≈ 28.54 km/h
Therefore, the bicycle is traveling approximately at a speed of 28.54 kilometers per hour.